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Alex
3 years ago
14

Using the following triangle, write a proof to verify that sinA/a=sinC/c

Mathematics
1 answer:
Sliva [168]3 years ago
6 0

Answer:

Proved: c\sin A=a\sin C\Rightarrow \frac{\sin A}{a}=\frac{\sin C}{c}

Step-by-step explanation:

Given: A triangle

To prove: \frac{\sin A}{a}=\frac{\sin C}{c}

Solution:

Trigonometry is a branch of mathematics that explains relationship between sides and angles of the triangle.

Sine of angle = side opposite to the angle / hypotenuse

In ΔADB,

\sin A=\frac{BD}{AB}=\frac{h}{c}\\\Rightarrow h=c\sin A\,\,\,(i)

In ΔBDC,

\sin C=\frac{BD}{BC}=\frac{h}{a}\\\Rightarrow h=a\sin C\,\,\,(ii)

From equations (i) and (ii),

c\sin A=a\sin C\\\frac{\sin A}{a}=\frac{\sin C}{c}

Hence proved

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<em>Complete Question:</em>

<em>The function shown models the depth d (in inches) of snow on the ground during the first 9 hours of a snowstorm, where t is the time (in hours) after the snowstorm begins. </em>

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<em>Function: d(t)= 1/2t+6</em>

Answer:

b = 6

m = \frac{1}{2}

Step-by-step explanation:

Given

d(t)= \frac{1}{2}t+6

Required

Determine the y intercept and the slope

y-intercept:

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A function has a format of:

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Where b represent the y intercept:

By comparison of d(t) = mt + b and d(t)= \frac{1}{2}t+6

b = 6

Slope:

A function has a format of:

d(t) = mt + b

Where m represent the slope

By comparison of d(t) = mt + b and d(t)= \frac{1}{2}t+6

m = \frac{1}{2}

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