A chair lift is to be built from the bottom of the mountain (point B) to the top (point T). A surveyor found the following measurements: ∠CBT = 21°, ∠BET = 17° and the distance BE = 780. What is the span of the chair lift? (The distance from B to T?) Round your answer to the nearest foot.
To find the span of the chair lift, we need to determine the distance from point B to point T.
We are given that ∠CBT = 21° and ∠BET = 17°, as well as the distance BE = 780.
To start, we can use trigonometric ratios. In this case, we'll use the tangent ratio since we have an angle and the opposite side.
In triangle BTE, we can use the tangent of ∠BET to find the length of BT:
tan(∠BET) = BT/BE
Rearranging the equation to solve for BT:
BT = BE * tan(∠BET)
Plugging in the values we know:
BT = 780 * tan(17°)
Using a calculator, we find BT ≈ 283.25.
Therefore, the span of the chair lift, which is the distance from B to T, is approximately 283.25 feet when rounded to the nearest foot.