Question

find the value of x, correct to 2 decimal places. 45^0 13 m

Explanation:

Step1: Identify the trigonometric relation

Since it's a right - triangle and one non - right angle is 45°, and we know the adjacent side to the 45° angle is 13 m. We can use the tangent function $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$ or the cosine function $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. Here we use the cosine function. $\cos45^{\circ}=\frac{13}{x}$.

Step2: Recall the value of $\cos45^{\circ}$

We know that $\cos45^{\circ}=\frac{\sqrt{2}}{2}$. So the equation becomes $\frac{\sqrt{2}}{2}=\frac{13}{x}$.

Step3: Solve for $x$

Cross - multiply to get $x\times\sqrt{2}=2\times13 = 26$. Then $x=\frac{26}{\sqrt{2}}$. Rationalize the denominator: $x=\frac{26\sqrt{2}}{2}=13\sqrt{2}\approx13\times1.414213562\approx18.38$.

Answer:

$18.38$