26. Law of sines, please give a step by step explanation
1 answer:
Answer:
174.6 ft
Step-by-step explanation:
It can be helpful to draw a diagram of the triangle we're concerned with. (See attached.)
We know the angle at the end of the shadow inside the triangle is 52°-22° = 30°. We assume the tree is growing straight up out of the hillside, so its angle with the hill inside the triangle is 90°+22° = 112°. Then the remaining angle between the shadow and the tree at the top of the tree is ...
180° -30° -112° = 38°
Now, we have the angle opposite the tree, and the angle opposite the known side length of the triangle (215 feet along the hill, AC in the diagram). This is enough information to usefully use the Law of Sines.
c/sin(C) = a/sin(A)
c = a(sin(C)/sin(A)) = (215 ft)(sin(30°)/sin(38°)) ≈ 174.6 ft
The height of the tree is about 174.6 feet.
You might be interested in
Answer:
Step-by-step explanation:
Isolate x on one side of the equation.
2(-2x-4) ← (Expand by using with distributive property.)
<u><em>DISTRIBUTIVE PROPERTY</em></u>
⇒ A(B+C)=AB+AC
⇒ A(B-C)=AB-AC
A=2
B=(-2x)
C=4
2(-2x)-2*4
-2*2x-2*4
-2*2x-2*4 (Solve.)
-2*2-2*4=-4x-8
Rewrite the equation problem.
10-x=-4x-8
10-x-10=-4x-8-10 (Subtract 10 from both sides.)
Solve.
-x=-4x-18
-x+4x=-4x-18+4x (Then, add 4x from both sides.)
3x=-18 (Solve.)
3x/3=-18/3 (Divide by 3 from both sides.)
-18/3 (Solve & Simplify.)
-18/3=-6
X=-6
Therefore, the correct answer is x=-6.