# Trig Right triangle Trigonometry

• TheKracken
In summary, the shortest distance from the ship to the shore can be found by dividing the 15 mile distance between observation points into two parts and using a system of linear equations to solve for the distance. Another approach is to calculate the rate at which the distance parallel to the shore reduces and use that to determine the distance from the ship to the shore.
TheKracken

## Homework Statement

As ship is anchor off a long straight shoreline that runs north and south. From twi observation points. 15 miles apart on shore the bearings of the ship are N 31 ° E and S 53 ° E. What is the shortest distance from the ship to the shore.

Sin θ Opp/ Hyp

## The Attempt at a Solution

I have drawn out the photo and it has a base of 15 miles and degree angles of 31, 53 and 96
I assumed the fastest route was a straight line back and that would cut the triangle into 2 different right triangles with their bases added together = 15 miles. I am confused if I should do a system of linear equations to make the straight line back to the shore being the unknown but then we have even more unknowns so I have no idea what to do. Any guidance for me please :( Iv'e got the Exam tomorrow and this is the last part of the chapter and most of it is still unknown for me.

TheKracken said:

## Homework Statement

As ship is anchor off a long straight shoreline that runs north and south. From twi observation points. 15 miles apart on shore the bearings of the ship are N 31 ° E and S 53 ° E. What is the shortest distance from the ship to the shore.

Sin θ Opp/ Hyp

## The Attempt at a Solution

I have drawn out the photo and it has a base of 15 miles and degree angles of 31, 53 and 96
I assumed the fastest route was a straight line back and that would cut the triangle into 2 different right triangles with their bases added together = 15 miles. I am confused if I should do a system of linear equations to make the straight line back to the shore being the unknown but then we have even more unknowns so I have no idea what to do.
This is how I would go, as well. You can divide up the 15 mile distance between the two stations as a and 15 - a. Call the distance from the shore to the ship d.
Write two equations in the two unknowns.
Solve.
TheKracken said:
Any guidance for me please :( Iv'e got the Exam tomorrow and this is the last part of the chapter and most of it is still unknown for me.

Here is another way, find the rate that the distance parallel to the shore between the sides of the triangle reduces, then use that to find the distance. If this is confusing, you should ignore this suggestion...

## What is Trigonometry?

Trigonometry is a branch of mathematics that deals with the study of triangles and the relationships between their sides and angles.

## What is a right triangle?

A right triangle is a triangle with one angle measuring 90 degrees.

## What are the three main trigonometric functions?

The three main trigonometric functions are sine, cosine, and tangent. These functions represent the ratio of the sides of a right triangle.

## How do I use trigonometry to solve a right triangle?

To solve a right triangle using trigonometry, you can use the trigonometric ratios (sine, cosine, and tangent) to find the missing side lengths or angles.

## What are some real-world applications of right triangle trigonometry?

Right triangle trigonometry is used in various fields such as engineering, physics, architecture, and navigation. It can be used to calculate distances, heights, and angles of objects in real-world situations.

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