Plsssss helppppp

Question

Thank you for your help. Here is a link to the problem: Link to image of problem

Answer 1

Hi Lia,

Step 1:

Find the measure of the 3rd angle in the triangle. It is easy to see that we can fill in the 3rd angle of the right triangle on the left in this figure. Since all three angles in a given triangle must sum to 180°, we can find the 3rd angle by subtracting the measure of the other two angles from 180°:

measure of 3rd angle = 180°- 90°- 28°

= 62°

Step 2:

Use soh•cah•toa to write possible equations for finding side length x. Since we now have all three angles in the triangle, we can make several equations using soh•cah•toa:

Using the 28° angle, we have:

sinθ = opposite/hypotenuse ⇒ sin28° = x/23.8 NOT an answer choice, so we'll keep going

tanθ = opposite/adjacent ⇒ tan28° = x/21 also NOT an answer choice

Using the 62° angle that we found in Step 1, we have:

cosθ = adjacent/hypotenuse ⇒ cos62° = x/23.8 this is answer choice A- correct

Hope that helps!