Question

Given that the hypotenuse of this right triangle is 25 cm long and that tan(θ) = 3find the values of x and y, accurate to the nearest tenth.

Answer 1

Answer:x ≈ 7.9; y ≈ 23.7

Explanation:

The right triangle above you can use SOHCAHTOA and determine that tanθ =

y

x

. Replacing tanθ with 3 you get

3 =

y

x

3x = y

Then use the Pythagorean Theorem to

x2 + y2 = 252. Replace y with 3x

x2 + 9x2 = 625

10x2 = 625

x2 =

625

10

x =

25

10

= 7.9

Since,

y = 3x

y = 3(7.9) = 23.7

Answer 2

The tangent of an angle is the opposite side divided by the adjacent side of the triangle, relative to the angle. By tan theta = 3, it means that, the adjacent side is thrice as long as the opposite side.

3a = o

Then, using Pythagorean's theorem:

25² = a² + o²
Substituting o,
25² = a² + (3a)²
25² = a² + 9a²
25² = 10a²
a = 7.9 cm

Then, 3(7.9) = o = 23.7 cm

So, the opposite side is 23.7 cm and the adjacent side is 7.9 cm.