Question

Using the triangle theorem solve this triangle.​

Answer 1

Answer:

OK THIS IS A BIGGY....c = 8

Step-by-step explanation:

First, find b.

using the pythagorean theorem, a² + b² = c²

to find b using an angle, do b = √(c² - a²)

then, b = a * tan(β)

(β is the angle 30°)

So, b = 6.928

Then, plug it into the pythagorean theorem

4² + 6.928² = c²

16 + 47.997184 = c²

63.997184 = c²

√63.997184 = √c

c = 7.99982399806

Rounded is 8 :)

Hope this helps! Please mark as brainliest :)

Answer 2

Answer:

b = 4$\sqrt{3}$ , c = 8

Step-by-step explanation:

Using the sine ratio in the right triangle and the exact value

sin30° = $\frac{1}{2}$ , then

sin30° = $\frac{opposite}{hypotenuse}$ = $\frac{4}{c}$ = $\frac{1}{2}$ ( cross- multiply )

c = 8

Using Pythagoras' identity in the right triangle

b² + 4² = 8²

b² + 16 = 64 ( subtract 16 from both sides )

b² = 48 ( take the square root of both sides )

b = $\sqrt{48}$ = $\sqrt{16(3)}$ = 4$\sqrt{3}$