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3 years ago

9 60° A) x = 18, y=9V6 B) x=9V3, y=9V3 C) x = 18, y=9V3 D) x =9V3, y=9V6

Mathematics

1 answer:

lesantik [10]3 years ago

7 0

Answer:

C. x = 18, y = 9 $\sqrt{3}$

Step-by-step explanation:

In a 30-60-90 triangle,

longer leg = $\sqrt{3}$ (shorter leg)

hypontenuse = 2(shorter leg)

In your case, the shorter leg = 9

therefore, y = 9 $\sqrt{3}$ and x = 2(9) = 18

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2 years ago

In the figure, triangle CAE is an enlargement of triangle CBD with scale factor of 4/3. The area of the smaller triangle is 9cm2

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16 cm^2

Step-by-step explanation:

Given

$\triangle CAE$ -- Bigger Triangle

$\triangle CBD$ -- Smaller Triangle

$k = \frac{4}{3}$ --- Scale factor

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Required

Determine the area of CAE

The area of triangle CBD is:

$A_1 = \frac{1}{2}bh$

$\frac{1}{2}bh = 9$

The area of CAE is:

$A_2 = \frac{1}{2}BH$

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$B = \frac{4}{3}b$ and

$H = \frac{4}{3}h$

The above values is the dimension of the larger triangle (after dilation).

So, we have:

$A_2 = \frac{1}{2}*\frac{4}{3}b * \frac{4}{3} * h$

$A_2 = \frac{1}{2}*\frac{4}{3} * \frac{4}{3} *b* h$

$A_2 = \frac{1}{2}*\frac{16}{9} *b* h$

Re-order

$A_2 = \frac{16}{9}*\frac{1}{2}* b* h$

$A_2 = \frac{16}{9}*\frac{1}{2}bh$

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