SOHCAHTOA Mountain Task 3

Question

Timmy Tangent and Susie Sine are on opposite sides of the base on Eastern Peak Mountain Between them is their base lodge, that is directly under the peak of the mountain which is 1,208.91 meters tall. The angle of elevation for Susie (on eastern base) to the peak is 70 degrees. And for Timmy (on the western side of the base) is 80 degrees of elevation to the top peak of the mountain.

Answer 1

1,208.91 meters

is the height of a triangle with two angles 70 and 80 degrees at the base,

angle at the top = 30 degrees = pi/6 radians

653.171 meters= the base of the triangle = the distance between Susie and Timmy

1286.495 meters is the distance from Susie to the peak

1227.559 meters is the distance from Timmy to the peak

Timmy is closer to the lodge and to the peak than Susie

Timmy has the 80 degree view of the peak

1227.559Cos80 = the distance from Timmy to the lodge = 1208.91Cot80 = about 213 meters

1286.495Cos70 = the distance from Susie to the lodge = 1208.91Cot70= about 440 meters

distance between Timmy and Susie = about 213+440 = 653 meters

either use a calculator with trig functions, or use an online website for "triangle calculations" plug in height and two angles and out pops the 3 sides of the triangle, along with endless other information about the triangle.

The title of your task 3, SOHCAHTOA stands for

Sine = opposite side over hypotenuse

Cosine= adjacent side over hypotenuse

Tangent = opposite side over adjacent side