Question

Trigonometric ratios

Answer 1

Answer:

$\boxed {\boxed {\sf x \approx 41}}}$

Step-by-step explanation:

Remember the three trigonometric ratios:

• sinθ= opposite/hypotenuse
• cosθ=adjacent/hypotenuse
• tanθ=opposite/adjacent

Examine the triangle. We have an angle measuring 59°.

The side measuring 35 is opposite the angle. x is the hypotenuse because it is the longest side.

Since we have the opposite side and the hypotenuse, we use sine.

$sin \theta= \frac {opposite}{hypotenuse}$

$sin 59=\frac{35}{x}$

Now, solve for x by isolating the variable. We can cross multiply.  Multiply the first numerator by the second denominator. Then, multiply the first denominator by the second numerator.

$\frac {sin59}{1}=\frac{35}{x}$

$sin59*x=35*1$

$sin59*x=35$

x is being multiplied by sin 59. The inverse of multiplication is division. Divide both sides by sin59.

$\frac {sin59*x}{sin59}=\frac {35}{sin59}$

$x= \frac {35}{0.8571673007}$

$x=40.8321689$

Let's round to the nearest whole number.

• 40.8321689

The 8 in the tenths place tells us to the 0 to a 1.

$x \approx 41$

The hypotenuse of the triangle is approximately 41.