Question

The top of a tree makes angles s and t with points K and L on the ground, respectively, such that the angles are complementary. Point K is x meters and point L is y meters from the base of the tree.
1. In terms of x and y, find the height of the tree. Include your calculations.
2. If m∠t = 40° and y = 8 meters, calculate the height of the tree, rounded to two decimal places.

Answer 1

1. In terms of x and y, the height of the tree is $h = y \times tan \ t^\circ$ and$h = x \times tan \ s^\circ$

2. The height of the tree is 6.71 meters

Trigonometry

From the question, we are to determine the height of the tree in terms of x and y

Using SOH CAH TOA, we can write that

$tan \ t^\circ =\frac{h}{y}$

∴ $h = y \times tan \ t^\circ$

Also,

$tan \ s^\circ =\frac{h}{x}$

∴ $h = x \times tan \ s^\circ$

2. If m∠t = 40° and y = 8 meters,

Then, the height of the tree

h = 8 × tan40°

h = 6.71 meters

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Hence, the height of the tree is 6.71 meters

Lear more on Trigonometry here: brainly.com/question/15977788

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