The answers are:
First image:
The answer is the second option, the angles is
Second image:
The answer is the third option:
Third image:
The length of the adjacent leg is the first option:
Fourth image:
The answer is the fourth option,
Fifth image:
The answer is the fourth option, DF (hypothenuse) is equal to 25 units.
<h2>Why?</h2>To solve these problems, we need to use the following trigonometric identities and the Pythagorean Theorem, since we are working with right triangles.
Pythagorean Theorem:
So, solving we have:
First image:
We are given a right triangle that has the following lengths:
Then, calculating we have:
Hence, the answer is the second option, the angles is
Second image:
We are given a right triangle that has the following lengths:
Then calculating the sin ratio, we have:
Thence, the answer is the third option:
Third Image:
We are given the following information:
Then, calculating one of the angle legs, since both will have the same length, using the sine trigonometric identity, we have:
Hence, the answer is the first option the length of the adjacent leg is
Fourth image:
We are given the following information:
To calculate the angle at the B vertex, first, we need to calculate the angle at the C vertex, and then, calculate the B vertex by the following way:
Since the sum of all the interior angles of a triangle are equal to 180°, we have that:
So, calculating the angle at the C vertex, we have:
Then, calculating the angle at the B vertex, we have:
Hence, the answer is the fourth option,
Fifth image:
We are given the following information:
Now, to calculate the distance DF (hypothenuse) we need to use the Pythagorean Theorem:
Then, substituting we have:
Hence, the answer is the fourth option, DF (hypothenuse) is equal to 25 units.
Have a nice day!