Question

How do you solve this?

Answer 1

P = 24 cm

q = 20.7846 cm

Explanation:

Answer:

Sides:

a = 12 cm

b = 24 cm

c = 20.7846 cm

Angles:

A = 30 °

B = 90 °

C = 60 °

Other:

P = 56.7846 cm

s = 28.3923 cm

K = 124.708 cm²

r = 4.3923 cm

R = 12 cm

Agenda:

A = angle A

B = angle B

C = angle C

a = side a

b = side b

c = side c

P = perimeter

s = semi-perimeter

K = area

r = radius of inscribed circle

R = radius of circumscribed circle

Given the size of 2 angles and 1 side opposite one of the given angles, you can calculate the sizes of the remaining 1 angle and 2 sides.

use the Sum of Angles Rule to find the other angle, then use The Law of Sines to solve for each of the other two sides.

Answer 2

• q = 12√3
• p = 24

Explanation:

The ratios of side lengths, shortest to longest, in a 30°, 60°, 90° triangle are ...

1 : √3 : 2

Since your shortest side is 12, the other two sides are ...

12 : q : p = 12 : 12√3 : 24

q = 12√3

p = 24

_____

Alternate solution

You can also solve this using trig ratios, as described for you in answer to one of your other questions.

12/q = tan(30°) . . . . q = 12/tan(30°) = 12√3

12/p = sin(30°) . . . . p = 12/sin(30°) = 24