Could someone please check my solution-Thank you-DRWLS helped me set it up and I solved it, I think
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
sin 38 = .6157
.6157 = 150/x
150/.6157 = 243.6
I set this up from the info below that drwls provided
Algebra II - drwls, Friday, January 7, 2011 at 2:25pm
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.
Algebra II-please check - Joseph, Friday, January 7, 2011 at 2:32pm
correct.
Thank you
To solve this problem, you need to use trigonometry. Here's how you can set it up:
1. Draw a diagram with a right-angled triangle. Place Jessie at the top of the triangle (the peak of the mountain), his bike at the ground level, and the base of the triangle, representing the distance from Jessie to his bike.
2. Label the height of the mountain (which is 150 feet) and the angle of elevation (which is 38 degrees).
3. Since we are given the sine of the angle and we want to find the distance, we can use the sine ratio: sin(angle) = opposite/hypotenuse.
4. In this case, the opposite side is the height of the mountain (150 feet) and the hypotenuse is the distance between Jessie and his bike (which we want to find).
5. Substituting the values into the equation, we have sin(38) = 150/x, where x is the distance between Jessie and his bike.
6. Now, solve for x. Multiply both sides of the equation by x to isolate x on one side: x * sin(38) = 150.
7. Divide both sides of the equation by sin(38) to solve for x: x = 150 / sin(38).
8. Use a calculator to evaluate sin(38) ≈ 0.6157.
9. Now, divide 150 by 0.6157 to find the value of x: x ≈ 243.6.
Therefore, the distance between Jessie and his bike is approximately 243.6 feet.