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3 years ago

Solving a right triangle (round to the nearest tenth) ‼️‼️‼️

Mathematics

1 answer:

harkovskaia [24]3 years ago

5 0

Answer:

see explanation

Step-by-step explanation:

The sum of the 3 angles in a triangle = 180°

Subtract the sum of the given angles from 180 for B

B = 180° - (90 + 47)° = 180° - 137° = 43°

-------------------------------------------------------------

tan47° = $\frac{opposite}{adjacent}$ = $\frac{a}{14}$

Multiply both sides by 14

14 × tan47° = a, thus

a ≈ 15.0 (to the nearest tenth )

---------------------------------------------------------------

cos47° = $\frac{adjacent}{hypotenuse}$ = $\frac{14}{c}$

Multiply both sides by c

c × cos47° = 14 ( divide both sides by cos47° )

c = $\frac{14}{cos47}$ ≈ 20.5 ( to the nearest tenth )

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Question:

A translation is applied to the triangle where A(1, 4) , B(2, -2) , and C(-3, 2). The image is the triangle that has vertices A′(5, 4) , B′(6, -2) , and C′(1, 2).

Answer:

$(x,y) ==>$ $(x + 4,y)$

Step-by-step explanation:

Given

$A = (1,4)\\B = (2,-2)\\C = (-3,2)$

$A' = (5,4)\\B' = (6,-2)\\C' = (1,2)$

From the translation of triangle ABC to A'B'C',

It will be observed that the y coordinates of both triangle remain unchanged.

This implies that triangle ABC is translated on the x coordinates alone.

Considering the x coordinates of A and A', we have:

$1 + k = 5$

Make k the subject

$k = 5 - 1$

$k = 4$

When 4 is added to the x coordinates of B and C, it gives the x coordinates of B' and C'.

Hence, the rule of translation is:

$(x,y) ==>$ $(x + 4,y)$

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4 years ago

Which polynomial expression represents the area of the outer most square tile, shown below?

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ANSWER

${x}^{2} - 6x + 9$

EXPLANATION

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