Question

Right triangles to find the exact length of:

T
30°
14 in
a) TI = in
60°
R

Answer 1

a) TI = 7√3 in

b) IR = 7 in

Step-by-step explanation:

Using cosine rule:

`\sf cos(x) = (adjacent)/(hypotenuse)`

`\hookrightarrow \sf cos(30) = (TI)/(14)`

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

`\hookrightarrow \sf TI = 7√(3)`

Using sine rule:

`\sf sin(x) = (opposite)/(hypotenuse)`

`\hookrightarrow \sf sin(30) = (IR)/(14)`

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

`\hookrightarrow \sf IR = 7`