# Trigonometry

A cat, sitting on top of a tree, spots a dog and a firefighter, both on flat ground below. From the cat's point of view, the dog is 10m south, at an angle of depression of 65 degrees, and the firefighter is some distance east of the tree, at an angle of depression of 50 degrees. How far is the firefighter from the dog?

1. 👍
2. 👎
3. 👁
1. The height h of the tree is given by

h/10 = tan 65°

Now, having h, you can get the distance f of the firefighter:

f/h = cot 50°

Now, the distance d between the dog and the firefighter is

d^2 = 10^2+f^2

1. 👍
2. 👎
2. vd

1. 👍
2. 👎

## Similar Questions

1. ### Physics

The magnitude of the momentum of a cat is p. What would be the magnitude of the momentum (in terms of p ) of a dog having two times the mass of the cat if it had the same speed as the cat? What would be the magnitude of the

2. ### math

Carlos purchased 6 dog leashes and 6 cat brushes for \$45.00 for Clarita to use while pampering the pets. Later in the summer he purchased 3 additional dog leashes and 2 cat brushes for \$19.00. Based on this information, figure out

3. ### Science

A cat is walking down a sidewalk and spots a dog in a nearby yard. The cat strats to run in the opposite direction and then quickly climbs a tree. Which of the the following changes most accurately describes the movement of the

4. ### Algebra

List all subsets of the following set: {dog, cat, fish} A. {dog}; {Cat}; {fish} B. {dog}; {Cat}; {fish}; {dog,cat}; {dog,fish} C {}; {dog}; {cat}; {fish}; {dog,cat}; {dog,fish}*** D {}; {dog}; {cat}; {fish}; {dog,cat}; {dog,fish};

1. ### math

Mrs. Bollo's second grade class of thirty students conducted a pet ownership survey. Results of the survey indicate that 8 students own a cat, 15 students own a dog, and 5 students own both a cat and a dog. How many of the

2. ### math

Carlos purchased 6 dog leashes and 6 cat brushes for \$45.00 for Clarita to use while pampering the pets. Later in the summer he purchased 3 additional dog leashes and 2 cat brushes for \$19.00. Based on this information, figure out

3. ### physics

A cat is being chased by a dog. Both are running in a straight line at constant speeds. The cat has a head start of 3.3 m. The dog is running with a speed of 9.0 m/s and catches the cat after 6.7 s. How fast did the cat run? I see

4. ### math

A dog starts chasing a cat when they are 12 meters apart. For every 7 meters that the dog runs, the cat runs 4 meters. How far does the dog have to run to catch up to the cat?

1. ### physics

A cat climbs 20 m directly up a tree. What is the horizontal component of the cat’s displacement? Answer in units of m.

2. ### statistics help

The branch manager of an outlet (Store 1) of a nationwide chain of pet supply stores wants to study characteristics of her customers. In particular, she decides to focus on two variables: the amount of money spent by customers and

3. ### math

From 70 feet away from the base of a tree on level ground, the angle to the top of a tree is 60⁰. What is the height of the tree? What is the approximate distance from the vantage point to the top of the tree, to one decimal

4. ### science

1.a modern train traveling at a constant speed around a circular track has a constant velocity true or false 2.which of the following would be affected if a soaring eagle change direction but remained at a constant speed?