Question

In a Right Angled Triangle,one of the acute angles is two-thirds of the other. Find the angles of the triangle​

Answer 1

Answer:

The angles are 54° and 36°

Step-by-step explanation:

In a Right Angled Triangle, one of the acute angles is two-thirds of the other.

Let's assume the other acute angle is x°

According to the problem:

2x/3 + x = 90

=> 2x + 3x = 270 [multiplying both sides of the equation by 3]

=> x = 270/5 = 54

and 2x/3 = 36

Answer 2

Answer:-

The angles of the triangle are 90° , 36° and 54°

Step-by-step explanation:-

To Find:-

• The angles of the triangle ......(?)

Solution:-

Let the triangle be ABC, and ∠A be 90° , ∠B be x and ∠C be $\sf{ \dfrac{2}{3}x}$

By angle sum property,

$\implies \: \sf{{90 \degree} + x + \dfrac{2}{3}x } = {180 \degree}$

$\implies \: \sf{x + \dfrac{2}{3}x } = {180 \degree - \: {90 \degree}}$

$\implies \: \sf{x + \dfrac{2}{3}x = {90 \degree}}$

$\implies \: \sf{\dfrac{3x + 2x}{3} = {90 \degree}}$

$\implies \: \sf{ \dfrac{5x}{3} = {90 \degree}}$

By cross Multipcation,

$\implies \: \sf{5x = 270}$

$\implies \: \sf{x = \dfrac{270}{5} }$

Dividing 270 with 5

$\implies \: \sf{x = 54}$

$\underline{ \sf{ \therefore \: The \: \: vaule \: \: of \: \: "x" \: \: is \: \: 54}}$

Now, Let's find the angles:-

We have assumed ∠B as x , and got x as 54

∴ ∠B = 54°

and we have assumed ∠C as $\sf{ \dfrac{2}{3}x}$, Now, the measure of ∠C is

$\implies \: \sf{ \dfrac{2}{3} \times 54}$

$\implies \: 3 \times 18$

$\implies \: {36 \degree}$

Now, Verification

$\implies \: {90 \degree}+{36 \degree}+{54 \degree}={180 \degree}$

$\implies \: {90 \degree}+{90 \degree}={180 \degree}$

$\implies \: {180 \degree}={180 \degree}$

L.H.S = R.H.S

Hence, Verified !