Question 1:
The first thing we must do for this case is to find the length of the sides of the triangle.
We then have the following trigonometric relations:
First side:
sine (30) = a / 7
a = 7 * sine (30)
a = 7/2
Second side:
sine (60) = b / 7
b = 7 * sine (60)
b = (7/2) * root (3)
Then, the perimeter of the triangle is:
P = 7 + 7/2 + 7/2 * (root (3))
P = 21/2 + 7/2 * (root (3))
Answer:
21/2 + 7/2 * (root (3))
option 4
Question 2:
We have the following relationship:
Tan (x) = 15
Clearing the value of x we have:
x = atan (15)
x = 86.18592517
Rounding out the nearest hundredth we have:
x = 86.19 degrees
Answer:
x = 86.19 degrees
option 4