# Trig

Find the length of a chord intercepted by a central angle of 25 degrees in a circle of radius 30 feet

1. 👍
2. 👎
3. 👁
1. let the length of the chord be 2x ft
Drop a perpendicular from the central vertex to the chord
then sin 12.5 = x/30
x = 30sin12.5
2x = 60sin12.5 = 12.9864

or by cosine law:
let the length of the chord be c
c^2 = 30^2 + 30^2 - 2(30)(30)cos25
= 168.64598..
c = 12.9864 , same as above

1. 👍
2. 👎

## Similar Questions

What is the arc length if the central angle is 225 degrees and the radius of a circle is 3 cm? pls help. i don"t get it

2. ### maths

a 4 cm long chord subtends a central angle of 60° . the radial segment of this circle is

a) Determine the measure of the central angle that is formed by an arc length of 5 cm in a circle with a radius of 2.5cm. Express the measure in both radians and degrees, correct to one decimal place. b) Determine the arc length

4. ### pre calcalus

a circle with 4 inch radius, find length of arc when intercepted by central angle of 240 degrees

1. ### Math

Which of the following values best approximates of the length of c in triangle ABC where c = 90(degrees), b = 12, and B = 15(degrees)? c = 3.1058 c = 12.4233 c = 44.7846 c = 46.3644 In triangle ABC, find b, to the nearest degree,

2. ### math

Find the length of the arc on a circle of radius r intercepted by a central angle θ. (Round your answer to two decimal places.) Radius r: 20 feet Central Angle θ: π/4 Arc Length s: radians

3. ### mathematics

For each of the following, tell how many non congruent triangles PQR fit the given description, and find the size of angle Q. Make a separate diagram for each case. (a) p = 3, q = 5, angle P = 27 degrees (b) p = 8, q = 5, angle P

4. ### Maths

AB is a chord with centre O and radius 4 cm. AB is of length 4 cm and divides the circle into two segments. Find d area of minor segment. A chord PQ of length 12cm suntends an angle of 120 degree at the centre of a circle. Find

1. ### Trigonometry

Determine the measure of the central angle if the length of the chord intercepted by the central angle of a circle of radius 20 inches is 16 inches.

2. ### Mathematics

A chord AB of length 2 cm is drawn in a circle of radius 3 cm. A diameter BC is constructed, and the tangent from C is drawn. The chord AB is extended to meet the tangent at D. Find the length of AD.

3. ### geometry

A circle has a radius of 3 feet and a central angle DEF that measures 60°. What is the length of the intercepted arc DF? Use 3.14 for pi and round your answer to the nearest tenth.