Question

The diagram shows a right-angled triangle. +o 11 cm Find the size of angle x. Give your answer correct to 1 decimal place. 6 cm​

Answer 1

Answer:

28.6°

Step-by-step explanation:

To find the size of angle $x$, we can use the trigonometric ratio tangent, which is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle in a right triangle.

Given:

• Opposite side ($O$) = 6 cm
• Adjacent side ($A$) = 11 cm

We can use the formula for tangent:

$\tan(x) = \dfrac{O}{A}$

Substitute the given values:

$\tan(x) = \dfrac{6}{11}$

Now, to find $x$, take the inverse tangent (arctan) of both sides:

$x = \arctan\left(\dfrac{6}{11}\right)$

Using a calculator, we find:

$x \approx 28.610459665965$

$x \approx 28.6^\circ \textsf{(in 1 decimal place)}$

So, the size of angle $x$ is approximately $28.6^\circ$.