The cosine of ∠ D is the ratio of the length of the leg adjacent ∠ D to the length of the hypotenuse.
cos D=Adjacent/Hypotenuse ⇒ cos D=6/10
By the definition of the inverse cosine, the inverse cosine of 610 is the measure of ∠ D. To find it we can use a calculator.
To find m∠ E, recall that the acute angles of a right triangle are complementary. Therefore, m∠ D and m∠ E add to 90^(∘).
m∠ D+m∠ E=90^(∘)
Now, we can substitute the approximated measure of ∠ D in our equation and find the measure of ∠ E.
53.1^(∘) +m∠ E≈ 90^(∘) ⇔ m∠ E≈ 36.9^(∘)
Side Lengths
Finally we can find the measure of d. To do it we can use the Pythagorean Theorem.
d^2+e^2=f^2
Let's substitute the known lengths, e= 6 and f= 10, into this equation to find d.
