Given a right triangle with a side of length 4 and a hypotenuse of length 7, find the measure of the two acute angles. (Round to the nearest hundredth.)
One side length of a right triangle is 4 and the hypotenuse is 7.
Then
sin(θ)=4/7, and
θ = sin-14/7.
(you will need to use the calculator for finding θ).
Similarly, the other angle can be calculated from:
φ = 90°-θ
thank you so much.. it really helped but i have one more,
The hypotenuse of a right triangle is 5 inches. If one leg is 2 inches, find the degree measure of each angle.
A. 42.4° and 47.6° B.12.2° and 77.8°
C. 23.6° and 66.4° D.16.7° and 73.2°
This is almost the same problem as the previous.
One side length of a right triangle is 2 and the hypotenuse is 5.
Then
sin(θ)=2/5, and
θ = sin-12/5.
(you will need to use the calculator for finding θ).
Similarly, the other angle can be calculated from:
φ = 90°-θ
To find the measure of the two acute angles in a right triangle, we can use trigonometric ratios. In this case, we are given the length of one side and the hypotenuse.
Let's label the side of length 4 as the "adjacent" side and the hypotenuse of length 7 as the "hypotenuse."
The trigonometric ratio we can use is the cosine function, which is defined as the ratio of the adjacent side to the hypotenuse:
cos(angle) = adjacent/hypotenuse
Plugging in the values we have, we can solve for the angle:
cos(angle) = 4/7
To find the value of the angle, we can use the inverse cosine function (also known as the arccosine function) on both sides of the equation:
angle = arccos(4/7)
Using a calculator or a math software, we can find the value of the angle as approximately 46.57 degrees.
Since we are looking for the measure of two acute angles, we know that the sum of these two angles is 90 degrees (as angles in a right triangle add up to 90 degrees).
Therefore, to find the second acute angle, we subtract the previously found angle from 90 degrees:
second angle = 90 degrees - 46.57 degrees
Calculating this, we find the second acute angle to be approximately 43.43 degrees.
So, the two acute angles in the right triangle with a side length of 4 and a hypotenuse of 7 are approximately 46.57 degrees and 43.43 degrees.