Question

Given that the hypotenuse of this right triangle is 25 cm long and that tan(Θ) = 3 Find the values of x and y, accurate to the nearest tenth. A) x ≈ 7.9; y ≈ 23.7 B) x ≈ 23.7; y ≈ 7.9 C) x ≈ 7.9; y ≈ 26.4 D) x ≈ 26.4; y ≈ 79.1

Answer 1

The wording of this problem indicates that there was an illustration.  Could you possibly share that illustration?

Working without an illustration:

If tan theta = 3, then tan theta = opp/adj = 3/1.  This tells us that the opp side is 3 times as long as is the adj. side.  Let x be the shorter side, i. e., let x represent the adjacent side; then y is the longer side and represents the opposite side.

Then y = 3x (the opp side is 3x the adj side in length).

Applying the Pyth. Thm.    a^2 + b^2 = c^2,

x^2 + (3x)^2 = hyp^2 = (25 cm.)^2

So x^2 + 9x^2 = (625 cm^2)

10x^2 = 625 cm^2, or x^2 = (625 cm^2) / 10 = 62.5 cm^2

x = 7.91 cm.  Therefore, y = 3(7.91) = 23.72 cm.

We were supposed to round off these answers to the nearest 10th cm.
Therefore, x = 7.9 cm and y = 23.7 cm

Would that be A, B, C or D?

Answer 2

Answer:

Step-by-step 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

x ≈ 7.9; y ≈ 23.7