Question

In right triangle PQR, if sinP=5/13, then tanP= 5/12 12/13 12/5

Answer 1

Answer:

A

Step-by-step explanation:

Given sinP = $\frac{5}{13}$ = $\frac{opposite}{hypotenuse}$

Then the right triangle has a hypotenuse of 13 and a leg 5

Use Pythagoras' identity to find the other leg x ( adjacent)

x² + 5² = 13²

x² + 25 = 169 ( subtract 25 from both sides )

x² = 144 ( take the square root of both sides )

x = $\sqrt{144}$ = 12 , hence

tanP = $\frac{opposite}{adjacent}$ = $\frac{5}{12}$

Answer 2

Is a right triangle => P ∈ (0,90]

sinP = 5/13 => cos²P = 1 - sin²P =>

=> cos²P = 1 - 25/169 = 144/169 =>

=> cosP = +12/13 (because P ∈ (0,90])

=> tanP = sinP / cosP = (5/13)/(12/13) =

= 5/12

=> tanP = 5/12