Question

right triangles to find the exact length of:
T
30°
14 in
a) TI = in
60°
R

Answer 1

Answer:

a) TI = 7√3 in

b) IR = 7 in

Explanation:

Using cosine rule:

$\sf cos(x) = \dfrac{adjacent}{hypotenuse}$

$\hookrightarrow \sf cos(30) = \dfrac{TI}{14}$

$\hookrightarrow \sf TI = 14cos(30)$

$\hookrightarrow \sf TI = 7\sqrt{3}$

Using sine rule:

$\sf sin(x) = \dfrac{opposite}{hypotenuse}$

$\hookrightarrow \sf sin(30) = \dfrac{IR}{14}$

$\hookrightarrow \sf IR = 14sin(30)$

$\hookrightarrow \sf IR = 7$