Question

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Answer 1

Check the picture below.

now, bear in mind that, there are 60minutes in 1 degree, so 23' is just 23/60 degrees or about 0.38 degrees.

and 29' is just 29/60 degrees or about 0.48 degrees.

so 16°23' is about 16.38°, and 49°29' is about 49.48°

$\bf tan(16.38^o)=\cfrac{200}{a+b}\implies a+b=\cfrac{200}{tan(16.38^o)} \\\\\\ \boxed{b=\cfrac{200}{tan(16.38^o)}-a} \\\\\\ tan(49.48^o)=\cfrac{200}{b}\implies \boxed{b=\cfrac{200}{tan(49.48^o)}}\\\\ -------------------------------\\\\ \cfrac{200}{tan(49.48^o)}=\cfrac{200}{tan(16.38^o)}-a\\\\\\a=\cfrac{200}{tan(16.38^o)}-\cfrac{200}{tan(49.48^o)}$

make sure your calculator is in Degree mode.

Answer 2

The distance covered by the boat is $\boxed{489.67{\text{ feet}}}.$

Further explanation:

The Pythagorean formula can be expressed as,

$\boxed{{H^2} = {P^2} + {B^2}}.$

Here, H represents the hypotenuse, P represents the perpendicular and B represents the base.

The formula for tan of angle a can be expressed as

$\boxed{\tan a = \frac{P}{B}}$

Explanation:

The perpendicular AB. The length of AB is $200{\text{ feet}}.$

The angle of depression is $\angle ACB = {14^ \circ }52'.$

One degree has 60 minutes.

${1^ \circ } = 60'$

$\begin{aligned}\angle ACB &= 49 + \frac{{29}}{{60}}\\&= 49 + 0.48\\&= 49.48\\\end{aligned}$

The angle ADB is $\angle ADB = {16^ \circ }23'.$

$\begin{aligned}\angle ADB&= {16^ \circ }23' \\&= 16 + \frac{{23}}{{60}}\\&= {16.38^ \circ }\\\end{aligned}$

In triangle ABC.

$\begin{aligned}\tan\left( {{{49.48}^\circ }} \right)&=\frac{{200}}{{BC}}\\1.13&= \frac{{200}}{{BC}}\\BC &= \frac{{200}}{{1.13}}\\BC &= 177{\text{ feet}}\\\end{aligned}$

In triangle ABD.

$\begin{aligned}\tan \left( {{{16.38}^ \circ }} \right)&= \frac{{200}}{{BD}}\\0.30&= \frac{{200}}{{BD}}\\BD&= \frac{{200}}{{0.30}}\\BD &= 666.67{\text{ feet}}\\\end{aligned}$

The distance boat can travel can be obtained as follows,

$\begin{aligned}DC& = BD - BC\\&= 666.67 - 177\\&= 489.67{\text{ feet}}\\\end{aligned}$

The distance covered by the boat is $\boxed{489.67{\text{ feet}}}.$

Kindly refer to the image attached.

Learn more:

1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.

2. Learn more about equation of circle brainly.com/question/1506955.

3. Learn more about range and domain of the function brainly.com/question/3412497

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Trigonometry

Keywords: perpendicular, person watching boat, top, lighthouse, angle of depression, angle of elevation, 200 feet tall, travel, sides, right angle triangle, triangle, altitudes, hypotenuse, on the triangle, hypotenuse, trigonometric functions.