Question

What is the length of AC ? Round to the nearest tenth.



10.5 m
12.3 m
18.3 m
21.4 m

Answer 1

In this right triangle, side AC is adjacent to the reference angle we were given.  That's our unknown.  The other side is the side opposite the reference angle, so we need a trig ratio that relates the side adjacent to the side opposite which is tangent.  Setting up our ratio we have this: $tan(55)= \frac{15}{x}$ and $x= \frac{15}{tan(55)}$.  Do that on your calculator to find that side AC (x) = 10.5, first choice above.

Answer 2

The length of AC is equal to 10.5m

Data;

• AC = ?
• BC = 15m
• Angle = 55 degrees

Trigonometric Ratio

To solve this problem, we have to apply trigonometric ratio SOHCAHTOA here;

Since we have the value of opposite side, angle and we are looking for the adjacent, we can use tangent of the angle to find AC
$tan\theta = \frac{opposite}{adjacent}$

Let's substitute the values and solve for AC

$tan 55 = \frac{15}{AC} \\AC = \frac{`15}{tan55} \\AC = 10.5m$

From the calculations above, the length of AC is equal to 10.5m

Learn more on trigonometric ratio here;

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