Question

Solve for x. Round to the nearest tenth, if necessary.

Answer 1

Hi there!

1. Trigonometric Ratio

• For this question, we will be knowing legs or sides of the right triangle and its ratio. Trigonometric Ratio or Trigonometry is very useful when it comes to solve for legs or sides. Because it has something to do with angles.

Currently, there are 6 Trigonometric Ratios. 2 ratios are the main topic which are sine and cosine. Both can be shortened as sin, cos. While the other 4 ratios are defined by these two ratios.

2. Adjacent, Hypotenuse, Opposite

• There are 3 sides in a right triangle. Opposite is a side or length of a triangle that is opposite of a specific angle. For example in the picture. CD is opposite of 65 degrees. ED is opposite of angle C.
• Adjacent is a leg or we can call it a base of right triangle.
• Hypotenuse is the longest side of right triangle according to Pythagorean Theorem. It is also the opposite of right angle.

3. Using Cosine Ratio

• Cosine Ratio is defined as adjacent to hypotenuse or adjacent/hypotenuse. Since we focus on the 65 degree. We can conclude that the adjacent side is x and the hypotenuse side is 7.

Cosine Ratio is:

$\large \boxed{ \tt{ cos 65 \degree= \frac{x}{7} }}$

For this part, use the calculator to find the value of cos65 degrees. When you put cos65 degree in a calculator, you should get 0.42261826... round to the nearest tenth as we get 0.4

Hence, the new equation is:

$\large{0.4 = \frac{x}{7} }$

4. Solve The Equation

• The best way to deal with decimal number when solving the equation is to multiply the whole equation by 10. Because we want to turn 0.4 to 4 which will be easier in solving the equation.

$\large{0.4 \times 10 = \frac{x}{7} \times 10} \\ \large{4 = \frac{10x}{7} }$

Multiply 7 both sides to get rid of the denominator.

$\large{4 \times 7 = \frac{10x}{7} \times 7} \\ \large{28 = 10x}$

Divide both sides by 10 so we can finally isolate x.

$\large{ \frac{28}{10} = \frac{10x}{10} } \\ \large{ \frac{28}{10} = x}$

Since the denominator is 10. We can convert to the decimal as 2.8

$\large \boxed{ \tt{2.8 = x}}$

Because you want the nearest tenth then 2.8 is your answer!

5. Final Answer

• x = 2.8