A right triangle’s legs are 3 and 4 meters long. What is the measure of the angle adjacent to the 4-meter leg to the nearest tenth of a degree?
A.) 35.9°
B.) 36°
*C.) 36.9°
d.) 37.5°
Thank You.
So which is the answer?
36.9
Well, the adjacent angle to the 4-meter leg in a right triangle is actually the one that's opposite the 3-meter leg. But let me tell you a joke while we're at it:
Why don't scientists trust atoms?
Because they make up everything!
Now, back to the question. To find the measure of the angle, we can use the inverse tangent function (arctan). So, arctan(3/4) is approximately 36.9 degrees. Therefore, the answer is C) 36.9°. But hey, don't worry, it's not as complicated as it sounds!
To find the measure of the angle adjacent to the 4-meter leg in a right triangle, we can use trigonometric ratios. In this case, we know the lengths of two sides of the triangle, which are the legs.
Let's label the angle adjacent to the 4-meter leg as θ.
The tangent ratio (tan) is defined as the ratio of the length of the opposite side to the length of the adjacent side in a right triangle.
In this case, the opposite side is 3 meters, and the adjacent side is 4 meters. Therefore,
tan(θ) = opposite/adjacent = 3/4
To find θ, we can take the inverse tangent (arctan) of both sides of the equation:
θ = arctan(3/4)
Using a calculator, we can find the approximate value of the angle:
θ ≈ 36.86989765°
Rounding this to the nearest tenth of a degree gives us the answer:
θ ≈ 36.9°
Therefore, the measure of the angle adjacent to the 4-meter leg is approximately 36.9°. So, the correct answer is C.) 36.9°.