Question

at needs to determine the height of a tree before cutting it down to be sure that it will not fall on a nearby fence. The angle of elevation of the tree from one position on a flat path from the tree is Upper H equals 60 degrees commaH=60°, and from a second position Upper L equals 20 feetL=20 feet farther along this path it is Upper B equals 40 degrees .B=40°. What is the height of the​ tree?

Answer 1

Answer:

32.6 feet

Step-by-step explanation:

The computation of the height of the tree is shown below:

Data provided in the question

One position H = 60 degree

Second position L = 20

B = 40 degree

Based on the above information, the calculations are as follows

In triangle ZWX,

$\frac{h}{x}=tan(60^{\circ}) => x=\frac{h}{tan(60^{\circ})}$

In triangle ZWY

$\frac{h}{x+L}=tan(40^{\circ}) => h=tan(40^{\circ})(x+20) => x=\frac{h}{tan(40^{\circ})}-20$

Now from equation 1 and equation 2

$x=\frac{h}{tan(60^{\circ})}=\frac{h}{tan(40^{\circ})}-20$

i.e

$20=\frac{h}{tan(40^{\circ})}-\frac{h}{tan(60^{\circ})} => h[1.1917535926-0.57735026919]=20$

Hence,

$h=\frac{20}{[1.1917535926-0.57735026919]}$

= 32.55190728

= 32.6 feet

Hence, the height of the tree is 32.6 feet