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Law of Sines

Law of Sines

Assessment

Presentation

•

Mathematics

•

11th Grade

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Practice Problem

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Medium

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CCSS
HSG.SRT.D.10, HSG.SRT.C.8, HSG.SRT.D.11

Standards-aligned

Created by

Okapi Zebraffe

Used 106+ times

FREE Resource

9 Slides • 4 Questions

1

Law of Sine

Introduction

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2

Introduction

Novy Most, the emblematic bridge in the city of Bratislava (Pozsony) is the largest obe-pillar bridge on earth. The pillar leans back in an angle of 109° to compensate for the wieght of the bridge. The fixation point of the longest cabel is 200 m away from the pillar foot. The said cabel forms an agle of 16° with the bridge body. Compute the length of the cabel.

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3

Multiple Choice

Can you use the known expression for sine?

1

yes

2

no

4

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5

Multiple Choice

Any other practical formula using trigonometry?

1

Yes, indeed

2

No, sorry

6

Trigonometric Area Formula


 T=x⋅200⋅sin⁡16°2T=\frac{x\cdot200\cdot\sin16°}{2}  

 T=y⋅200⋅sin⁡109°2T=\frac{y\cdot200\cdot\sin109°}{2}   T=x⋅y⋅sin⁡55°2T=\frac{x\cdot y\cdot\sin55°}{2}  

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7

T is the same value, let's make use of it


 y⋅200⋅sin⁡109°2=x⋅y⋅sin⁡55°2\frac{y\cdot200\cdot\sin109°}{2}=\frac{x\cdot y\cdot\sin55°}{2}  

 y⋅200⋅sin⁡109°=x⋅y⋅sin⁡55°y\cdot200\cdot\sin109°=x\cdot y\cdot\sin55°  

 200⋅sin⁡109°=x⋅sin⁡55°200\cdot\sin109°=x\cdot\sin55°  

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8

En route to the law 1


 sin⁡109°sin⁡55°=x200\frac{\sin109°}{\sin55°}=\frac{x}{200}  

 sin⁡16°sin⁡55°=y200\frac{\sin16°}{\sin55°}=\frac{y}{200}  

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9

Law of sines - The sine rule

 sin⁡αsin⁡β=ab\frac{\sin\alpha}{\sin\beta}=\frac{a}{b} 

  sin⁡αsin⁡γ=ac\frac{\sin\alpha}{\sin\gamma}=\frac{a}{c}  

 sin⁡βsin⁡γ=bc\frac{\sin\beta}{\sin\gamma}=\frac{b}{c}   

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10

Multiple Select

Can you use the Law of Sines for right triangles?

1

Yes, of course

2

Not at all

11

The sine rule 

with 90° at vertex C

 (sin⁡αsin⁡β=ab)\left(\frac{\sin\alpha}{\sin\beta}=\frac{a}{b}\right) Makes no change...

  sin⁡α1=ac\frac{\sin\alpha}{1}=\frac{a}{c}  :) Hurray! ;P

 sin⁡β1=bc\frac{\sin\beta}{1}=\frac{b}{c}   :) Hurray! ;P

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12

Homework

Find the of unknown data for

- the length of side(s) and

- the measure of angle(s)

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13

Poll

Can we somehow find the the measure of the angles in a triangle knowing only side lengths?

The rule of sines must help

The rule of sines cannot help

Hoping for a new tool

Please let me practice more of these sines things

pattern-tertiary

Law of Sine

Introduction

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