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The acute angles of a right angled triangle are in the ratio 2:3. Find the angles of the triangle?

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°

and 54

°

°

and 54

°

°

and 64

°

°

and 74

°

answer is A.

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Detailed Solution

Concept-The triangle is a right angle triangle, which means that one of its angles is

90 degrees,

while its other two angles are sharp (smaller than 90 degrees). The acute angle of the triangle is now divided in a

2 : 3 ratio

, and the formula to get the angles is:
A triangle's total number of angles equals 180.
As we can see from the question, there are two acute angles, and the ratio of each angle is given. In order to get the two acute angles, let's add a random variable to the ratios in order to change them into acute angles. Let's thus assume that the two variables' common unknown is x and that the angles are

2 x and 3 x .

As a result, using the angles from the formula provided in the clue, we determine the triangle's total number of angles to be:

\Rightarrow 2 x + 3 x + 90 \circ = 180 \circ

Since the triangle has a right angle, the third angle is 90 degrees.

\Rightarrow 5 x + 90 \circ = 180 \circ

\Rightarrow 5 x = 180 \circ - 90 \circ \Rightarrow x = 18 \circ

Now that we know the two acute triangle's common unknown variable, we can determine its two angles as

2 x and 3 x,

where we may obtain their values as

2 x = 218

and 3x=318 by setting the value of

x = 18 .

36 and 54

As a result, the triangles' two sharp angles 36 and 54 as well as their third 90 are given. Therefore, "36 and 54 with the third one as 90" is the right response.
Hence, option 1 is correct.

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