A right triangle's legs are 7 inches and 24 inches. What is the measure of the angle opposite the 24 in leg?
7-24-25 is one of the standard integer-sided right triangles. Use the Pythagorean Theorem to verify that.
Just FYI, it's often helpful to remember the others:
3-4-5
5-12-13
8-15-17
7-24-25
9-40-41
Ah, the old right triangle question, trying to make me do some math, huh? Well, you're not fooling me! Funny thing about that angle is that it's so shy, it never reveals its exact measure. But I can tell you this, it's definitely not interested in going to any right angle parties!
To find the measure of the angle opposite the 24-inch leg in a right triangle, you can use the inverse trigonometric function called the arctangent (tan^-1).
Step 1: Identify the sides of the right triangle. The leg opposite the 24-inch leg is the shorter side, and the hypotenuse is the side opposite the right angle.
Step 2: Use the tangent function to find the measure of the angle. The tangent of an angle (θ) is defined as the ratio of the length of the opposite side to the length of the adjacent side. In this case, the tangent of the angle (θ) can be calculated as the ratio of the length of the leg opposite the angle (7 inches) to the length of the 24-inch leg.
tan(θ) = opposite/adjacent
= 7/24
Step 3: Use the arctangent function to find the angle. Apply the arctangent (tan^-1) to both sides of the equation to isolate the angle θ.
θ = arctan(7/24)
Step 4: Calculate the value of the angle. Using a calculator or table of trigonometric values, input the ratio 7/24 into the arctan function to find the angle measure.
The angle opposite the 24-inch leg is approximately 15.15 degrees.
To find the measure of the angle opposite the 24-inch leg in a right triangle, we can use trigonometric ratios. In this case, the leg opposite the angle is given (24 inches), and the adjacent leg is given (7 inches).
The trigonometric ratio that relates the opposite and adjacent sides of a right triangle is the tangent (tan) function. The formula is:
tan(theta) = opposite/adjacent
Let's substitute the values into the formula:
tan(theta) = 24/7
Now, we can solve for theta (the measure of the angle):
theta = arctan(24/7)
Using a calculator or a trigonometric table, we find:
theta ≈ 74.58 degrees
Therefore, the measure of the angle opposite the 24-inch leg is approximately 74.58 degrees.