Do these three segments make a right triangle? 16m, 30m, and 34m
2 answers:
Answer:
Yes, the three segments 16,30,34 make a right triangle.
Step-by-step explanation:
The three segments are the following 16,30, and 34.
We will use the Pythagorean Theorem to find out if the three numbers can make a right triangle.
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When we have 3 numbers given, our largest number is the hypotenuse.
So 34 is our hypotenuse, so we substitute it as the c in our formula.
And our a^2 and b^2 are 16 and 30!
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Our formula verifies that the three segments provided can make a right triangle.
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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.
