Precal Help?

Question

Two teams survey a mountain. Survey team A measures the angle of inclination to the mountain peak to be 15 degrees,
and survey team B measures it to be 25 degrees. If the two teams are 4776.4 feet from each other, what is the height
of the mountain to the nearest foot?

 

Thank you

Answer 1

Two teams survey a mountain:

Survey team A measures the angle of inclination to the mountain peak to be 15 degrees.

Survey team B measures it to be 25 degrees.

The two teams are 4776.4 feet from each other.

What is the height of the mountain to the nearest foot?

Use the following formulas to solve the math word problem.

Law of Sines: a/sin A = b/sin B = c/sin C

sin (A-B) = sin A cos B -cos A sin B

_____________________________________________

Solve for the angle at the peak of the mountain ( triangle)

Step 1 The sum of angles in a triangle is 180 degrees

The angle at the peak is 180 degrees - 25 degrees - 15 degrees = 140 degrees

Find the distance from team B to the peak using the Law of Sines.

Step 2

Let (d) be the distance from team B to he peak.

d /sin 15 degrees = 4776.4/sin 140 degrees

d = 4776.4 x sin 15 degrees divide by sin 140 degrees

sin x 15 degrees =.2588190451 sin x 140 degrees =.6427876097

d = 4776.4 x .2588 divided by .6428 = 1922.1 feet

Step 3

Find the height of the mountain.

Let h = height of mountain.

sin 25 degrees = (h) height divided by distance d=1922.1 ft

Solve for h = d times (sin 25 degrees) = .4226182617

h = 1922.1 times 0.4226 = 812.3145609 roundoff as specified

h = 812.3 feet (round to nearest foot) = 812 feet

Solution

Height of Mountain = 812 feet

I hope the mathematical calculations (step by step approach) was helpful. Please let me know if you require any more assistance. If anyone in my neighborhood is interested in setting up an in-person math tutoring session. I look forward to hearing from them. Have an amazing day. Doris H.