From the top of a mountain 150 feet high, Jessie stands at the safety rail on the edge and looks below. The angle of elevation from his bike on the ground to Jessie is 38 degrees, how far is Jessie from his bike.Please help me to set this up
Thank you
Draw a figure with a right angle triangle connecting Jessie, his bike and the base of the cliff.
38 degrees = arcsin 150/X,
where X is the distance you seek. (It is the hypotenuse of that triangle).
Solve that equation for X
sin38 = 150/X is one way to do it.
sin 38 = .6157
.6157 = 150/x
150/.6157 = 243.6
Correct
To find the distance between Jessie and his bike, you can use trigonometric ratios. In this case, we can use the tangent function.
Let's denote the distance between Jessie and his bike as "x".
The angle of elevation from the bike on the ground to Jessie is 38 degrees. This means that the tangent of the angle is equal to the ratio of the opposite side (the height of the mountain) to the adjacent side (the distance between Jessie and his bike).
So, we have: tan(38°) = 150 feet / x
To solve for x, we can rearrange the equation: x = 150 feet / tan(38°)
Now we can calculate the value of x using a scientific calculator:
x ≈ 150 feet / tan(38°)
x ≈ 150 feet / 0.781286047
x ≈ 192.103 feet
Therefore, Jessie is approximately 192.103 feet away from his bike.