Question

Find the value of x, rounded to the nearest tenth

Answer 1

Answer:

x=12.5

Step-by-step explanation:

The given triangle is a right angle triangle.

We cannot use the Pythagoras theorem as the lengths of all sides are not known. We will use triangular ratios here to solve the given problem.  

As it is clear from the diagram that x is the hypotenuse of the triangle and 11 is the length of the base. We will use a ratio in which base and hypotenuse are used.

So,

cos ⁡θ= base/hypotenuse

cos⁡ 28=11/x

x=11/cos⁡28  

x=11/0.8829

x=12.45

Rounding off to nearest 10

x=12.5

Answer 2

In every right triangle, a leg is given by the multiplication between the hypothenuse and the sine of the opposite angle, or the cosine of the adjacent one.

So, in this case, we have

$11 = x\cos(28)$

Solving for x, we have

$x = \dfrac{11}{\cos(28)}\approx 12.5$