Question

In the national park, the distance between the base of two cliffs is 312 feet. The angle of elevation from the base of the shorter cliff to the top of the taller cliff is 35 degrees. The angle of elevation from the base of the taller cliff to the top of the shorter cliff is 27 degrees. The tops of the two cliffs are joined by a bridge of length x. What is the length of the bridge, x, to the nearest foot?

a) 312 feet

b) 556 feet

c) 168 feet

d) 240 feet

Answer 1

To find the length of the bridge, we can use the concept of trigonometry. Let's find the length of side b and then apply the law of cosines to find the length of the bridge. Therefore, the length of the bridge is approximately 556 feet (option b).

Step-by-step explanation:

To find the length of the bridge, we can use the concept of trigonometry.

Let's draw a diagram to represent the situation:

B

/|

/ |

c / | a

/ |

/ |

A C

Here, A and B represent the tops of the two cliffs, and C represents the base of the shorter cliff. The distance between A and C is given as 312 feet.

Using trigonometry, we can find the length of the bridge (x) by finding the length of side b and then applying the law of cosines.

Let's find the length of side b:

tan(27°) = b/312

b = 312 * tan(27°)

b ≈ 168.06 feet

Now, let's apply the law of cosines:

x^2 = a^2 + b^2 - 2ab * cos(35°)

x^2 = 312^2 + (168.06)^2 - 2 * 312 * 168.06 * cos(35°)

x ≈ 555.75 feet

Therefore, the length of the bridge is approximately 556 feet (option b).