Question

Find the length of side AB. Give your answer to 1 decimal place. 12 cm 62° A B

Answer 1

Hey there!

To solve this problem, we will be using Trigonometric Ratio. Trigonometry is always helpful when it comes to finding a missing side with specific measure/angle.

1. Cosine Ratio

• Currently, there are 6 Trigonometric Ratios. But we will be talking about Cosine Ratio instead since it is what we will be using in your question! Cosine Ratio is defined as adjacent to hypotenuse or adjacent/hypotenuse. You know what adjacent and hypotenuse are right? If not then head to the next topic!

2. Adjacent and Hypotenuse

• Adjacent is basically the base of a triangle. It is basically drawn from right angle to any measure/angles.
• Hypotenuse is the longest side of a right triangle. It is also an opposite side of right angle.

Hope you understand this topic! If not, feel free to ask!

3. Solve The Problem

• Since our adjacent is length AB but we don't know its exact value. What we have to do is to determine AB as any variables which I will determine AB as "x".
• Next, we have the value of hypotenuse which is 12 cm.
• Then we also know the Cosine Ratio which is adjacent to hypotenuse.

Therefore, the equation for the problem is:

$\large{cos62 \degree = \frac{x}{12} }$

*cos is the short form of cosine*

At this part, we need a calculator to find the value of cos62 degrees. That's because it is not a degree like 0, 30, 45, 60 and 90 which can be found without a calculator.

When we put cos62 in a calculator, make sure to put it in degree mode since a calculator has two modes which are degree and radian.

When we put cos62 in, we should get 0.46947156... Because you want a one decimal place, we round the value up to the nearest tenth as we get 0.5 because 6 is greater than 5 and should be rounded up and not down. That makes the equation to:

$\large{0.5 = \frac{x}{12} }$

Oh well! Finally to the equation part. Whenever you have to solve the equation that has decimal numbers in it, the best way to deal with decimal numbers is to make them into a whole number or integer. But how? Simply multiply the whole equation by 10. Because 0.5×10 is 5 thus 0.5 becomes an integer after multiplying 10.

$\large{0.5 \times 10 = \frac{x}{12} \times 10} \\ \large{5 = \frac{10x}{12} }$

10x/12 can be simplified again.

$\large{5 = \frac{5x}{6} }$

Then we isolate x-value by multiplying 6 the whole equation.

$\large{5 \times 6 = \frac{5x}{6} \times 6} \\ \large{30 = 5x} \\ \large{x = 6}$

Huh, that's awkward! We want the answer in a 1 decimal place but seems like the answer for this is 6. Why? Well that is not an exact answer, but more like an approximation. Because the value of cos62 degree is actually a repeating decimal and doesn't have exact value.

When we put the equation cos62 = x/12 in the equation and solve. It appears that the the answer is 5.63365875. Because we round up to nearest tenth, it gives an approximation to 5.63365875 instead.

Hence, the equation and value above is just a rounded to the whole number from 5.63365875.

Because you want a one place decimal. Hence,

4. Final Answer

• The length AB is 5.6 (rounded to nearest tenth)