yolo1143

27.11.2020 •

Mathematics

Number of tulips number of roses = 6:5 number of red tulipsinumber of yellow tulips = 3:4
Work out the proportion of the flowers that are red tulips.

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Ответ:

gordonandrea313

28.03.2022

Mathematics

The distance covered by the boat is $\boxed{556.71{\text{ feet}}}.$

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.

${1^ \circ } = 60'$

$\begin{aligned}\angle ACB&=14+\frac{{52}}{{60}}\\&= 14 + 0.87\\&= 14.87\\\end{aligned}$

The angle ABD is $\angle ADB={45^ \circ }10'.$

$\begin{aligned}\angle ADB &= {45^\circ }10' \\&= 45 + \frac{{10}}{{60}}\\&= 45 + 0.17 \\ &= {45.17^\circ }\\\end{aligned}$

In triangle ABC.

$\begin{aligned}\tan \left( {{{14.87}^\circ }} \right)&=\frac{{200}}{{BC}}\\0.26&= \frac{{200}}{{BC}}\\BC&= \frac{{200}}{{0.265}}\\BC &= 754.72{\text{ feet}}\\\end{aligned}$

In triangle ABD.

$\begin{aligned}\tan \left({48.217} \right)&= \frac{{200}}{{BD}}\\1.01&= \frac{{200}}{{BD}}\\BD&= \frac{{200}}{{1.01}}\\BD &= 198.01{\text{ feet}}\\\end{aligned}$

The distance boat can travel can be obtained as follows,

$\begin{aligned}DC &= BD- BC\\&= 754.72 - 198.01\\&= 556.71{\text{ feet}}\\\end{aligned}$

The distance covered by the boat is $\boxed{556.71{\text{ feet}}}.$

Kindly refer to the image attached.

Learn more:

1. Learn more about inverse of the

2. Learn more about equation of circle

3. Learn more about range and domain of the function

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.

Aperson is watching a boat from the top of a lighthouse. the boat is approaching the lighthouse dire

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Number of tulips number of roses = 6:5 number of red tulipsinumber of yellow tulips = 3:4 Work out the proportion of the flowers that are red tulips.