Question

The furthest angle of elevation to the top of the steeple was 20 degrees and the closest angle elevation to the church was 29 degrees. Each person is 1.7 meters tall from his feet to his eyeballs. Find the measure of angle ACB. (Hint: Find measure of angle ABC first).

A) 151 degrees
B) 9 degrees
C) 171 degrees
D) 20 degrees

Answer 1

The angle measure of ACB is 9 degrees

Answer: Option B

Explanation:

To find the solution to the given problem, first we need to look into the point B. It consists two angles and both of them are on a straight angle. So, this means that the sum of angle ABC and CBD is 180 degrees, that is

`\angle A B C+\angle C B D=180^(\circ)`

We know that
`\angle C B D=29^(\circ)`. Therefore

`\angle A B C+29^(\circ)=180^(\circ)`

`\angle A B C=180^(\circ)-29^(\circ)=151^(\circ)`

Now, in the triangle ABC, we know that all three angles must sum 180 degrees,

`\angle C A B+\angle A B C+\angle B C A=180^(\circ)`

`20^(\circ)+151^(\circ)+\angle B C A=180^(\circ)`

`\angle B C A=180^(\circ)-20^(\circ)-151^(\circ)=9^(\circ)=\angle A C B`

Therefore, the angle ACB is 9 degrees.