Ask question

Ask question

All categories

2 years ago

13

A person is watching a boat from the top of a lighthouse. The boat is approaching the lighthouse directly. When first noticed, t

he angle of depression to the boat is 14°52'. When the boat stops, the angle of depression is 45°10'. The lighthouse is 200 feet tall. How far did the boat travel from when it was first noticed until it stopped? Round your answer to the hundredths place.

1 answer:

tatyana61 [14]2 years ago

4 0

The boat's travel from when it was first noticed until it stopped is 554.89 ft.

<h3>What is trigonometry?</h3>

Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.

We have:

A person is watching a boat from the top of a lighthouse. The boat is approaching the lighthouse directly.

From the given information we can draw a right-angle triangle.

14°52' = 14 + 0.86 = 14.86 degree

45°10' = 45 + 0.16 = 45.16 degree

In the right-angle triangle ACD

tan14.86 = 200/AC

AC = 753.772 ft

In the right-angle triangle DBC:

tan45.16 = 200/CB

CB = 198.886 ft

AB = AC - CB

AB = 753.772 ft - 198.886 ft

AB = 554.886 ≈ 554.89 ft

Thus, the boat's travel from when it was first noticed until it stopped is 554.89 ft.

Learn more about trigonometry here:

brainly.com/question/26719838

#SPJ1

You might be interested in

The commercial for the new Meat Man Barbecue claims that it takes 10 minutes for assembly. A consumer advocate thinks that the c

Andrews [41]

Answer:

There is enough evidence to make the conclusion that the population mean amount of time to assemble the Meat Man barbecue is not equal to 10 minutes (P-value=0.009).

Step-by-step explanation:

We have to perform an hypothesis test on the mean.

The null and alternative hypothesis are:

$H_0: \mu=10\\\\H_1: \mu \neq 10$

The significance level is $\alpha=0.05$ .

The test statistic t can be calculated as:

$t=\frac{M-\mu}{s/\sqrt{N} } =\frac{11.2-10}{3.1/\sqrt{50} }=2.737$

The degrees of freedom are:

$df=N-1=50-1=49$

The P-value (two-tailed test) for t=2.737 and df=49 is P=0.00862.

This P-value (0.009) is smaller than the significance level, so the effect is significant. The null hypothesis is rejected.

There is enough evidence to make the conclusion that the population mean amount of time to assemble the Meat Man barbecue is not equal to 10 minutes.

7 0

3 years ago

What is the gcf of 30x^2 and 66x^5?

pantera1 [17]

Answer:

$6x^2$

Step-by-step explanation:

Express as product of prime factors.

$30x^2=2\times 3\times 5\times x^2$

$66x^5=2\times 3\times 11\times x^5$

The greatest common factor is the product of the least powers of the common factors.

The GCF is

$2\times 3\times x^2=6x^2$

4 0

3 years ago

Can someone please help me with this

krek1111 [17]

Step-by-step explanation:

0.1 repeating is 1/9, so the number is 4 1/9.

5 0

3 years ago

Simplify (Are all division)<br><br>2+4i<br>3i<br><br>3+2i<br>4+i<br><br>2i^11

Alla [95]

$We\ know:\ i=\sqrt{-1}\to i^2=-1$

$\dfrac{2+4i}{3i}=\dfrac{2+4i}{3i}\cdot\dfrac{3i}{3i}=\dfrac{6i+12i^2}{9i^2}=\dfrac{6i+12(-1)}{9(-1)}\\\\=\dfrac{6i-12}{-9}=\dfrac{2i-4}{-3}=\dfrac{4}{3}-\dfrac{2}{3}i$

$\dfrac{3+2i}{4+i}=\dfrac{3+2i}{4+i}\cdot\dfrac{4-i}{4-i}=\dfrac{(3+2i)(4-i)}{4^2-i^2}\\\\=\dfrac{(3)(4)+(3)(-i)+(2i)(4)+(2i)(-i)}{16-(-1)}=\dfrac{12-3i+8i-2i^2}{16+1}\\\\=\dfrac{12+5i-2(-1)}{17}=\dfrac{12+5i+2}{17}=\dfrac{14+5i}{17}=\dfrac{14}{17}+\dfrac{5}{17}i$

$2i^{11}=2i^{10+1}=2i^{10}i^1=2i^{2\cdot5}i=2i(i^2)^5=2i(-1)^5=2i(-1)=-2i$

$Used:\ (a+b)(a-b)=a^2-b^2$

6 0

3 years ago

2x − y = −4→10x − 5y = −20 3x 5y = 59→3x 5y = 59 13x = 39 which equation can replace 3x 5y = 59 in the original system and still

malfutka [58]

13x = 39 can replace 3x + 5y = 59 in the original system and still produce the same solution.

8 0

3 years ago