Question

Your family room has a sliding-glass door. You want to buy an awning for the door that will be just long enough to keep the Sun out when it is at its highest point in the sky. The angle of elevation of the rays of the Sun at this point is 70 $\degree$ , and the height of the door is 8 feet. Your sister claims you can determine how far the overhang should extend by multiplying 8 by tan 70 $\degree$

Answer 1

Your sister is not correct. You can determine how far the overhang should extend by dividing 8.

Explanation:

You can determine how far the overhang should extend by dividing

Observe the picture attached. You can identify that the angle A and the angle B are congruent (which means that they have equal measure).

Let be "CB" is the length in feet that the overhang should be in order to keep the Sun out when it is at its highest point in the sky.

You need to use the following Trigonometric Identity:

You can notice that, in this case:

Knowing these values you can substitute them into and then solve for "CB" in orde to find its value.

Therefore, your sisteter is not correct.

Answer 2

Answer: Your sister is not correct. You can determine how far the overhang should extend by dividing 8 by
`tan(70\°)`

Explanation:

The complete exercise is attached.

Observe the picture attached. You can identify that the angle A and the angle B are congruent (which means that they have equal measure).

Let be "CB" is the length in feet that the overhang should be in order to keep the Sun out when it is at its highest point in the sky.

You need to use the following Trigonometric Identity:

`tan\alpha =(opposite)/(adjacent)`

You can notice that, in this case:

`\alpha =70\°\\\\opposite=8\ ft\\\\adjacent=CB`

Knowing these values you can substitute them into
`tan\alpha =(opposite)/(adjacent)` and then solve for "CB" in orde to find its value.

You get:

`tan(70\°)=(8)/(CB)\\\\CB*tan(70\°)=8\\\\CB=(8)/(tan(70\°))\\\\CB=2.91`

Therefore, your sisteter is not correct.