Question

A tree growing on a hillside makes a 75° angle with the hill. From a point 80 feet up the hill, the angle of elevation to the top of the tree is 65° and the angle of depression to the bottom is 24°. Find the height of the tree.

Answer 1

Answer:

height of tree = 290.19 feet  

Step-by-step explanation:

given data

angle with the hill a = 75°

up the hill = 80 feet

elevation to top of tree =  65°

angle of depression to bottom = 24°

solution

we know that Sum of Property of Triangles  is

sum of the internal angles of a triangle =  180°   ............1

and

Sine Rule is

$\frac{A}{Sin(a)} = \frac{B}{Sin(b)} = \frac{C}{Sin(c)}$      .......................2

so here

angle with the hill a = 75°

and

sum of the angle of elevation and angle of depression is

b =  65°+ 24°

b = 89°

and we know

a + b + c = 180°  

so c will be

c = 180° - 89° - 75°  

c = 16°

so here we get height of the pine tree by equation 2 we get

$\frac{80}{Sin(16)} = \frac{B}{Sin(89)}$  

solve it we get

height of tree = 290.19 feet