Question

Ralph the monkey is looking down at a 59° angle from the top of a tree. There are bananas on the ground 12.4 ft from the base of the tree. If Ralph flies down from the tree at a diagonal path, shown in the diagram by x, what distance would he travel? Round to the nearest hundredth

Answer 1

Answer:

Ralph the monkey traveled 14.47 feet

Step-by-step explanation:

As shown in the picture below we are looking for the value of the hypotenuse which in this case is the diagonal distance Ralph the monkey would travel if he jumped at a 59° degree angle. Since we are given the angle 59° and the opposite side length, we can use the SIN operator to solve this problem.

$sin(x) = \frac{opposite}{hypotenuse}$

$sin(59) = \frac{12.4}{x}$

$\frac{1}{sin(59)} = \frac{x}{12.4}$ .....invert both fractions

$1.166 = \frac{x}{12.4}$

$14.47 = x$

We get a value of 14.47 ft for the hypotenuse, meaning that Ralph the monkey traveled 14.47 feet after jumping from the top of the tree at a 59° angle.

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Answer 2

This forms a right angled triangle and Ralph flies down the hypotenuse x,

so using trigonometry:-

sin 59 = 12.4 / x

x = 12.4 / sin 59

= 14.47 feet to nearest hundredth.