Measuring the height of a mountain can be very difficult as you cannot measure your horizontal distance to the point right below the top of the mountain. So you take two measurements, make a system of equations and solve the system. Here's your scenario. You are looking at a mountain and sight the top with an angle of elevation of 55 degrees. Then you walk 500 feet towards the mountain and take another measurement. This time, the angle of elevation is 65 degrees. Find the height of the mountain assuming that you are 5 feet tall.

Question

anonymous · Answer

|dw:1359694208693:dw|

so...
You can solve the length of side 'c' using sine law:
$$\frac{c }{ \sin 115 } = \frac{500}{\sin 10}$$
$$c \approx 2609.6 ft$$
You could try using pythagorean's theorem to solve for the mountain height, but there is still an unknown distance to the base of the mountain. Instead, just use plain old sine trig equation:
$$\sin \Theta = \frac{opposite}{hypoteneus}$$
$$2609.6 \sin 55 = height of mountain$$
but since we took our measurements off the ground, don't forget to add 5 ft to the height. : )

anonymous · Answer

so 2609.6 plus five?

anonymous · Answer

2609.6*sin 55 = 2137.7ft
then add 5, lol

anonymous · Answer

my  mistake, thank you very much.

anonymous · Answer

no problem, : )