Peggy is laying 60 ft from the base of a tree. The angle of elevation for her to see the top of the tree is 50º. Use a trigonometric ratio and calculator to find the
height of the tree to the nearest tenth of a foot.

The height of the tree is approximately 71.5 feet

Step-by-step explanation:

The given parameters are;

The angle of elevation to see the top pf the tree = 50°

The distance Peggy is laying from the base of the tree = 50 ft.

In order to answer the question using trigonometric ratio, we assume that the angle the tree makes with the ground is 90° that is the tree is perpendicular to the ground

Therefore, the line of sight to the top of the tree,  the height of the tree, and the distance from the base of the tree where Peggy is laying, forms a right triangle

Let, 's', represent the line of sight to the top of the tree, let 'h', represent the height of the tree, and let, 'd', represent the distance from the base of the tree where Peggy is laying

The third angle, θ, of the right triangle opposite 'd' is given by angle sum theorem of a triangle as follows;

θ = 180° - 90° - 50° = 40°

θ = 40°

By sine rule we have;

h/sin(50°) = d/(sin θ)

∴ h/sin(50°) = 60 ft./(sin 40°)

h = sin(50°) × 60 ft./(sin 40°) = 71.5052156 ft.

∴ The height of the tree, h ≈ 71.5 ft. by rounding to the nearest tenth

rx and sx

step-by-step explanation:

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