To find the value of x and the measure of angle E, we can use the trigonometric ratios in a right triangle.
Given that side DE (hypotenuse) is 10 and side FD (height) is 6, we can use the Pythagorean theorem to find side EF (base):
EF^2 = DE^2 - FD^2
EF^2 = 10^2 - 6^2
EF^2 = 100 - 36
EF^2 = 64
EF = √64
EF = 8
So, the measure of side EF (x) is 8.
To find the measure of angle E, we can use the sine ratio:
sin(E) = opposite/hypotenuse
sin(E) = FD/DE
sin(E) = 6/10
sin(E) = 0.6
To find the measure of angle E, we can take the inverse sine (sin^-1) of 0.6:
E = sin^-1(0.6)
E ≈ 36.87 degrees
Therefore, the value of x is 8 and the measure of angle E is approximately 36.87 degrees.
What are the value of x and the measure of <E to the nearest degree?
Right triangle D E F is shown with labeled sides. Side D E is the hypotenuse and it is labeled 10. Side E F is the base and it is labeled X. Side F D is the height and it is labeled 6. Angle E is opposite side F D.
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