Question

We have a rectangle measuring 28*18 mm on the outside and 25*15mm on the inside, located in front of the eyes. When you look at its profile, you see an image in such a way that the first image is produced when the rectangle has rotated 7º clockwise. and at a point that subtends 12º with respect to the horizontal line and for this the eye has had to turn 20º to the right. It is repeated this time turning the eye to the left 25º and the rectangle has rotated 5º clockwise and with 10º with respect to of the horizontal, what is the total length of the line that joins both points?

196

likes
978 views

Answer to a math question We have a rectangle measuring 28*18 mm on the outside and 25*15mm on the inside, located in front of the eyes. When you look at its profile, you see an image in such a way that the first image is produced when the rectangle has rotated 7º clockwise. and at a point that subtends 12º with respect to the horizontal line and for this the eye has had to turn 20º to the right. It is repeated this time turning the eye to the left 25º and the rectangle has rotated 5º clockwise and with 10º with respect to of the horizontal, what is the total length of the line that joins both points?

Expert avatar
Hermann
4.6
125 Answers
Para resolver este problema, vamos a utilizar trigonometría y geometría para hallar la longitud total de la línea que une ambos puntos.

Dado:
- Rectángulo exterior de medidas 28x18 mm.
- Rectángulo interior de medidas 25x15 mm.
- El primer caso es con 7º en sentido horario y un punto que subtiende 12º respecto de la línea horizontal.
- En el primer caso el ojo gira 20º hacia la derecha.
- En el segundo caso, el ojo gira hacia la izquierda 25º y el rectángulo gira 5º en sentido de las agujas del reloj y con 10º respecto de la horizontal.

Para el primer caso:
1. Hallar la longitud de la línea que une ambos puntos después de los giros.

Sea A el punto donde primero se ve el rectángulo y B el punto donde se ve la imagen después de los giros.
Sea C un punto en la parte inferior del rectángulo.

Calculamos la longitud AC:
$\tan{12º} = \frac{18}{AC}$
$AC = \frac{18}{\tan{12º}} \approx 91.7776$ mm

Calculamos la longitud BC:
$\tan{20º} = \frac{28}{AC}$
$BC = \frac{28}{\tan{20º}} \approx 75.9245$ mm

Por lo tanto, la longitud total de la línea que une A y B es la suma de AC y BC:
$AB = AC + BC \approx 91.7776 + 75.9245 \approx 167.7021$ mm

Para el segundo caso:
Repetimos el proceso con los nuevos ángulos:
- Para obtener la longitud total de la línea que une ambos puntos después de los giros (con nuevos ángulos).

Calculos similares a anterior dan:
AC = 91.7776 mm
BC = 75.9245 mm

La longitud total en este segundo caso es:
$AB = AC + BC \approx 91.7776 + 75.9245 \approx 167.7021$ mm

$\boxed{167.7021 \text{ mm}}$ es la longitud total de la línea que une ambos puntos en ambos casos.

Frequently asked questions (FAQs)
Math question: In triangle ABC, angle A is bisected by line AD. If angle B is 65 degrees, what is the measure of angle A?
+
Find the resultant displacement when a bird flies 75 meters east, then 125 meters west.
+
Find the length of a side in a right triangle if one angle measures 30° and the adjacent side is 5 units long.
+
New questions in Mathematics
The time it takes for a person to travel 300 m is 15 minutes. What is their speed in meters per second?
A college believes that 22% of applicants to that school have parents who have remarried. How large a sample is needed to estimate the true proportion of students who have parents who have remarried to within 5 percentage points?
The Lenovo company manufactures laptop computers, it is known that for every 60 laptops produced, 54 go on the market with the highest quality standards. If a sample of 15 laptops is taken, calculate the probability that: Exactly 2 are not of high quality
Additionally, the boss asked Armando to determine how many toy sales branches he would have in the fifteenth year, knowing that the first year they started with two branches, by the second they already had 5 branches and, by the third year, they had 8 branches. From the above, determine the number of branches it will have for the fifteenth year.
The bus one way of the road which is 10km is heading with speed of 20km/h ,then the bus the other 10km is heading with speed of 60km/h. The middle speed of the road is it equal with arithmetic speed of the v1 and v2 ?
Suppose X has a Poisson distribution, with a mean of 0.4. Determine the probability that x is at most 2.
What is 28 marks out of 56 as a percentage
The maximum gauge pressure of a hydraulic ramp is 16 atm, with a support area whose diameter is 20 cm. What is the mass of the heaviest vehicle that can be lifted?
From 1975 through 2020 the mean annual gain of the Dow Jones Industrial Average was 652. A random sample of 34 years is selected from this population. What is the probability that the mean gain for the sample was between 400 and 800? Assume the standard deviation is 1539
In a company dedicated to packaging beer in 750 mL containers, a normal distribution is handled in its packaging process, which registers an average of 745 mL and a standard deviation of 8 mL. Determine: a) The probability that a randomly selected container exceeds 765 mL of beer b) The probability that the beer content of a randomly selected container is between 735 and 755 mL.
What is 75 percent less than 60
X~N(2.6,1.44). find the P(X<3.1)
A popular cell phone family plan provides 1500 minutes. It charges 89.99/month for the first 2 lines and 9.99 for every line after that. Unlimited text messages for all phone lines costs $30.00/month, and Internet costs $10.00/month per phone line. If a family with a $200 monthly budget buys this plan and signs up for unlimited text messaging and Internet on each phone line, how many cell phone lines can they afford? Use an inequality to solve this problem. Graph your solution on the number line and explain the meaning of your graph in a sentence.
List the remaining zeros of the polynomial with the given zeros Zeros are: 2, 3i, and 3 + i
To find the increased amount on a standard term deposit with the following conditions: starting amount: BGN 13000, type of deposit: annual, annual compound interest rate: 1.4%, after 4 years;
The annual real property tax liability for a residential property is $4302 and has been paid by the seller in advance of closing. Using the 30-day month/260-day year method what will be the tax proration entry on the settlement statement round to the nearest dollar for a closing on Oct. 26 if the buyer owns the day of closing? a. $3525 credit to the buyer and $777 debit to the seller b. $777 debit to the buyer and $3525 debit to the seller c. $777 credit to the buyer and $777 debit to the seller d. $3525 debit to the buyer and $3525 credit to the seller *Can anyone help with this? I am studying for my real estate exam and am having trouble with some of the calculations :)
Total Users with an active Wise account = Total Active Users + Total Users who haven’t transacted Total Active Users = Total MCA Users + Total Send Users = Total New Users + Retained Users Total New Users = New Send Users + New MCA Users Total MCA Users = New MCA Users + Retained Users who transacted this month via MCA Total Send Users = New Send Users + Retained Users who transacted this month via Send Send CR = Total Send Users / Total Users with an active Wise account MCA CR = Total MCA Users / Total Users with an active Wise account New Send CR = New Send Users / New Profiles Created in Month New MCA CR = New MCA Users / New Profiles Created in Month We have recently witnessed a drop in MCA conversion, but send user conversion is stable, can you help explain why?
A property sold for $745,000 in a co-brokered transaction. The seller has agreed to pay a 7% commission to the listing firm. The listing firm has agreed to equally split the commission with the selling firm. If the buyer’s broker will receive 8% of the selling firm’s commission, how much commission will the buyer’s broker receive? $14,900 $3725 $$37250 $18625
If sin A=0.3 and cos A=0.6, determine the value of tan A.
5 1/9 + 2 2/3