Question

Math

Posted 5 months ago

```
Kapil's robot starts $70 \mathrm{~cm}$ from its charging base. It faces the base, then turns $60^{\circ}$ clockwise, as shown. Finally, the robot moves $50 \mathrm{~cm}$.
After moving, how far is the robot from the charging base?
Do not round during your calculations. Round your final answer to the nearest centimeter.
$\square$ $\mathrm{cm}$
```

Sign in to unlock the answer

Answer from Sia

Posted 5 months ago

Solution by Steps

step 1

Use the Law of Cosines to find the length of the unknown side opposite the 60° angle

step 2

The Law of Cosines formula is $c^2 = a^2 + b^2 - 2ab\cos(\gamma)$, where $c$ is the length of the side opposite the angle $\gamma$, and $a$ and $b$ are the lengths of the other two sides

step 3

Substitute the given values into the Law of Cosines formula: $c^2 = 70^2 + 50^2 - 2(70)(50)\cos(60°)$

step 4

Calculate the cosine of 60°, which is $\frac{1}{2}$

step 5

Substitute the cosine value into the equation: $c^2 = 70^2 + 50^2 - 2(70)(50)\left(\frac{1}{2}\right)$

step 6

Simplify the equation: $c^2 = 4900 + 2500 - 3500$

step 7

Calculate the value of $c^2$: $c^2 = 3900$

step 8

Take the square root of both sides to find $c$: $c = \sqrt{3900}$

step 9

Round the final answer to the nearest centimeter: $c \approx 62$ cm

Answer

The robot is approximately 62 cm from the charging base.

Key Concept

Law of Cosines

Explanation

The Law of Cosines is used to find the length of a side of a triangle when two sides and the included angle are known.

Not the question you are looking for? Ask here!

Enter question by text

Enter question by image

Upgrade to Asksia Pro

Join a AskSia's Pro Plan, and get 24/7 AI tutoring for your reviews, assignments, quizzes and exam preps.

Unlimited chat query usages

Strong algorithms that better know you

Early access to new release features

Study Other Question