1. ## Geometry

Can you please help me set up these two problems. I am having a difficult time getting started and knowing where to take the problem. Thanks

The "pitch" of a roof refers to the vertical rise measured against a standard horizontal distance of 12 inches. If the pitch of a roof is 5 in 12 (the roof rises 5 inches for every 12 horizontal inches), find the acute angle the roof makes with a horizontal line. Round your answer to one decimal place.

a. 65.4 o

b. 67.4 o

c. 24.6 o

d. 22.6 o

The distance between two buildings is 160 feet. You are standing on the roof of the taller building. You measure the angle of depression of the top and bottom of the shorter building. If the angles are 36.2 o and 71 o, respectively, find the height of the shorter building. Round to the nearest foot.

a. 465 feet

b. 348 feet

c. 117 feet

d. 582 feet

2. Originally Posted by d.darbyshire
...
The "pitch" of a roof refers to the vertical rise measured against a standard horizontal distance of 12 inches. If the pitch of a roof is 5 in 12 (the roof rises 5 inches for every 12 horizontal inches), find the acute angle the roof makes with a horizontal line. Round your answer to one decimal place.

a. 65.4 o
b. 67.4 o
c. 24.6 o
d. 22.6 o

The distance between two buildings is 160 feet. You are standing on the roof of the taller building. You measure the angle of depression of the top and bottom of the shorter building. If the angles are 36.2 o and 71 o, respectively, find the height of the shorter building. Round to the nearest foot.

a. 465 feet
b. 348 feet
c. 117 feet
d. 582 feet
Hello,

to solve such problems you should first make a diagram to describe the situation.

to 1.: let the angle be $\displaystyle \alpha$. Use the tangens:
$\displaystyle \alpha=\arctan \left( \frac{5}{12} \right) \approx 22.6198...^o$
$\displaystyle h=160 \cdot \tan(71^\circ)-160 \cdot \tan(36.2^\circ) \approx 347.57...$