Question

If anyone is good at right triangle trig word problems please help

Answer 1

The height of the hill is 131ft

See explanation in the photo

Answer 2

• 91 feet

Explanation:

Refer to attached picture

Let the base is b and the height of the hill is x.

For the smaller triangle we have:

• x/b = tan 39.3°

And for the bigger triangle:

• (x + 40)/b = tan 49.7°

Solve both equations for b:

• b = x/ tan 39.3°
• b = (x + 40)/tan 49.7°

Eliminate b and get the values of tan, solve for x:

• x/ tan 39.3° = (x + 40) / tan 49.7°
• x tan 49.7° = (x + 40) tan 39.3°
• x( 1.179) = x(0.819) + 40(0.819)
• x(1.179 - 0.819) = 32.76
• x = 32.76/0.36
• x = 91 feet (rounded to the nearest foot)