What is the length, in units, of segment cd?

Asked by maham237 @ 25/12/2020 in Mathematics viewed by 320 People

What is the length, in units, of segment CD?

Answered by maham237 @ 25/12/2020

Answer:

The answet is C.

Step-by-step explanation:

First, you have to find the angle of ACB using Sine Rule, sinθ = opposite/hypotenuse :

$\sin(θ ) = \frac{oppo.}{hypo.}$

$let \: oppo. = 4 \\ let \: hypo. = 5$

$\sin(θ) = \frac{4}{5}$

$θ = {\sin( \frac{4}{5} ) }^{ - 1}$

$θ = 53.1 \: (1d.p)$

Given that line AB is parallel to line CD so ∠C = 90°. Next, you have to find the angle of ACD :

$ACD = 90 - 53.1 = 36.9$

Lastly, you can find the length of CD using Cosine rule, cosθ = adjacent/hypotenuse :

$\cos(θ) = \frac{adj.}{hypo.}$

$let \: θ = 36.9 \\ let \: adj. = 5 \\ let \: hypo. = CD$

$\cos(36.9 ) = \frac{5}{CD}$

$CD \cos(36.9) = 5$

$CD = \frac{5}{ \cos(36.9) }$

$CD = 6.25 units\: (3s.f)$

Similar Questions

What is the length of segment sr units

Asked by maham237 @ 25/04/2021 in Mathematics viewed by 659 persons

What is the length of segment ns? 1 unit 2 units 4 units 6 units

Asked by maham237 @ 26/12/2020 in Mathematics viewed by 473 persons

What is the length of segment NS? 1 unit 2 units 4 units 6 units

What is the length of line segment kj? units units units units

Asked by maham237 @ 24/12/2020 in Mathematics viewed by 485 persons

What is the length of line segment KJ? A. 2√3 units B. 3√2 units C. 3√5 units D. 3√3 units

If the unit of length and force be increased

Asked by admin @ 17/08/2021 in Physics viewed by 379 persons

If the unit of length and force be increased four times, then the unit of energy isA. increased 4 times.B. increased 8 times.C. increased 16 times.D. decreased 16 times.

The unit of length velocity and force are doubled

Asked by admin @ 13/08/2021 in Physics viewed by 365 persons

The unit of length,velocity and force are doubled.Which of the following is the correct change in the other units?1.unit of time is doubled2.unit of mass is doubled3.unit of momentum is …

Find the approximate length of segment gh on the graph

Asked by maham237 @ 29/05/2021 in Mathematics viewed by 262 persons

What is the length of segment sr

Asked by maham237 @ 27/04/2021 in Mathematics viewed by 266 persons

Find the length of the segment

Asked by maham237 @ 06/01/2021 in Mathematics viewed by 241 persons

The length of the segment AD is 28 cm. The distance between the midpoints of segments AB and CD is 16 cm. Find the length of the segment BC .

What is the length of ? 9 units 12 units 15 units 18 units

Asked by maham237 @ 26/12/2020 in Mathematics viewed by 494 persons

What is the length of SR? 9 units 12 units 15 units 18 units

In circle a, ∠bae ≅ ∠dae. what is the length of be? 14 units 17 units 27 units 34 units

Asked by maham237 @ 25/12/2020 in Mathematics viewed by 519 persons

In circle A, ∠BAE ≅ ∠DAE. Circle A is shown. Line segments A B, A E, and A D are radii. Lines are drawn from point B to point E …

In circle d, ∠edh ≅ ∠edg. what is the length of jg? 4 units 5 units 6 units 9 units

Asked by maham237 @ 25/12/2020 in Mathematics viewed by 582 persons

In circle D, ∠EDH ≅ ∠EDG. What is the length of JG? 4 units 5 units 6 units 9 units

Draw a line segment of length 7 cm

Asked by admin @ 26/08/2021 in Math viewed by 410 persons

Draw a line segment AB of length 7 cm. Taking A as centre, draw a circle of radius 3 cm and taking 8 as centre, draw another circle of radius …

Draw a line segment of length 8 cm

Asked by admin @ 25/08/2021 in Math viewed by 334 persons

Draw a line segment AB of length 8 cm. Taking A as centre, draw a circle of radius 4 cm and taking B as centre, draw another circle of radius …

Draw a line segment of length 7.6 cm

Asked by admin @ 25/08/2021 in Math viewed by 320 persons

draw a line segment of length 7.6cm and divide in ratio 5:8 measure the two parts.give the justification of construction

Draw a line segment ab of length 5 cm

Asked by admin @ 20/08/2021 in Math viewed by 343 persons

draw a line segment a b of length 5 cm and at A and B construct line perpendicular to a b also draw the perpendicular bisector of a b are …

Most viewed questions in Mathematics

Unit 6 similar triangles homework 2 similar figures answer key

Asked by maham237 @ 25/06/2021 in Mathematics viewed by 18381 persons

All things algebra unit 7 polygons and quadrilaterals answer key

Asked by admin @ 30/09/2021 in Mathematics viewed by 8169 persons

Gina wilson all things algebra 2016 answer key unit 11

Asked by admin @ 07/11/2021 in Mathematics viewed by 5796 persons

Unit 1 geometry basics homework 4 angle addition postulate answers

Asked by maham237 @ 19/05/2021 in Mathematics viewed by 3940 persons

Unit 6 exponents and exponential functions homework 8 answer key

Asked by maham237 @ 03/01/2021 in Mathematics viewed by 3262 persons

The manager of a vacation resort believes that the ages

Asked by maham237 @ 19/07/2021 in Mathematics viewed by 2929 persons

What is 271 403 rounded to the nearest ten thousand

Asked by maham237 @ 24/07/2021 in Mathematics viewed by 2805 persons

Unit 1 geometry basics homework 3 angle relationships answer key

Asked by maham237 @ 21/05/2021 in Mathematics viewed by 2592 persons

Homework 2 parallelograms

Asked by maham237 @ 02/01/2021 in Mathematics viewed by 2507 persons

Why would a prism beat a sphere in a competition?

Asked by maham237 @ 13/01/2021 in Mathematics viewed by 2485 persons

John wants to send a letter to peter

Asked by maham237 @ 13/01/2021 in Mathematics viewed by 2470 persons

An artist sells a painting for 20.50 but uses 5.75

Asked by maham237 @ 24/06/2021 in Mathematics viewed by 2439 persons

Unit 4 congruent triangles homework 1 classifying triangles answer key

Asked by maham237 @ 10/06/2021 in Mathematics viewed by 2425 persons

Unit 4 congruent triangles homework 2 angles of triangles

Asked by maham237 @ 26/04/2021 in Mathematics viewed by 2082 persons

Compare the values of the 2s and 5s in 55220

Asked by maham237 @ 18/07/2021 in Mathematics viewed by 1800 persons