Question

In a right angled triangle , if half of the length of the hypoten use. Find the measure of the angle opposite to the side.​

Answer 1

Given:

In a right-angled triangle, if a side is half of the length of the hypotenuse.

To find:

The measures of the angle opposite to the side.​

Solution:

Let,

"ABC" → represents the triangle

"h" → represents the height of the triangle

"x" → represents the side of the triangle

A side is half of the length of the hypotenuse, so the equation will be,

$x = \frac{1}{2} h$  . . . . . Equation 1

Now, in ΔABC, by using the trigonometric ratios of a triangle, we get

$sin \:\theta = \frac{Opposite \:side}{Hypotenuse}$ . . . . [since we have to find the angle opposite to the given side]

$\implies sin \:\theta = \frac{x}{h}$

on substituting from equation 1

$\implies sin \:\theta = \frac{\frac{1}{2} h}{h}$

$\implies sin \:\theta = \frac{1}{2}$

on multiplying the sin inverse on both sides

$\implies sin^-^1(sin \:\theta) = sin^-^1(\frac{1}{2})$

$\implies \theta = sin^-^1(\frac{1}{2})$

∵ sin 30° = $\frac{1}{2}$

$\implies \bold{\theta = 30\°}$

Thus, the measure of the angle opposite to the side is → 30°.

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Answer 2

Answer:

Given:

In a right-angled triangle, if a side is half of the length of the hypotenuse.

To find:

The measures of the angle opposite to the side.​

Solution:

Let,

"ABC" → represents the triangle

"h" → represents the height of the triangle

"x" → represents the side of the triangle

A side is half of the length of the hypotenuse, so the equation will be,

 . . . . . Equation 1

Now, in ΔABC, by using the trigonometric ratios of a triangle, we get

. . . . [since we have to find the angle opposite to the given side]

on substituting from equation 1

on multiplying the sin inverse on both sides

∵ sin 30° =

Thus, the measure of the angle opposite to the side is → 30°.

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