Question

if x and y are the measures of complementary angles in a right triangle such that sin (y)=10 sqrt (2)/15 and tan (x) = 5/10 sqrt (2), label the sides of the right triangle

Answer 1

10\sqrt{2}, 15 and 5

Step-by-step explanation:

Given the following

Sin y = 10 sqrt (2)/15 and tan x = 5/10 sqrt (2)

According to SOH CAH TOA identity

Sin theta = opposite/hypotenuse

Comparing with Sin y = 10 sqrt (2)/15

opposite = 10\sqrt{2}

hypotenuse = 15

Get the third side which is the adjacent using the pythagoras theorem

hyp^2 = opp^2 + adj^2

15^2 = (10\sqrt{2})^2 + adj^2

225 = 100(2) + adj^2

225 = 200 + adj^2

adj^2 = 225-200

adj^2 = 25

adj = \sqrt{25}

adj = 5

Since the sides pf the triangle are the opposite, adjacent and hypotenuse, hence the sides of the trinagle are 10\sqrt{2}, 15 and 5