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3 years ago

Which pair of measurements is not equivalent?

Mathematics

1 answer:

Bingel [31]3 years ago

6 0

Answer:

750 mm, 7.5 cm

Step-by-step explanation:

Verify each case

case a) 2.5 km, 2,500 m

we know that

1 km ------> 1.000 m

2.5 km=2,500 m

therefore

The pair of measurements is equivalent

case b) 750 mm, 7.5 cm

we know that

1 cm ------> 10 mm m

7.5 cm=75 mm

therefore

<u>The pair of measurements is not equivalent</u>

case c) 3 m, 3,000 mm

we know that

1 m ------> 1.000 mm

3 m=3,000 mm

therefore

The pair of measurements is equivalent

case d) 120 cm, 1.2 m

we know that

1 m ------> 100 cm

1.2 m=120 cm

therefore

The pair of measurements is equivalent

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Answer:

(i) the other two sides are 6 and 6 $\sqrt{2}$

(ii) the other two sides are $\frac{4}{3} and \frac{8}{3}$

Step-by-step explanation:

(i) Sine: sin(θ) = Opposite ÷ Hypotenuse

Cosine: cos(θ) = Adjacent ÷ Hypotenuse

Tangent: tan(θ) = Opposite ÷ Adjacent

Here adjacent side = 6

opposite side = d

angle = 45°

other angles are 90° and 45°

tan (45) = Opposite ÷ Adjacent

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∴ d = 6 × 1 = 6

so opposite side = 6

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hypotenuse = $\sqrt{72}$

= 6 $\sqrt{2}$

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(ii) here adjacent side = 4√3

angle = 30°

other angles are 90° and 60°

opposite side = d

tan ( 30) = opposite ÷ adjacent

$\frac{1}{\sqrt{3}}$ = d ÷ 4√3

$\frac{1}{\sqrt{3}}$ = d × ( $\frac{\sqrt{3}}{4}$ )

3 d = 4

therefore d = $\frac{4}{3}$

therefore opposite side = $\frac{4}{3}$

Hypotenuse ² = opposite side ² + adjacent side²

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therefore hypotenuse = $\sqrt{\frac{64}{9}}$

= $\frac{8}{3}$

the other two sides are $\frac{4}{3} and \frac{8}{3}$

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Find the area of triangle ABC. Give your answer correct to 1 decimal place AC=7 Cb=12 a=72 degrees b=59 degrees

Tems11 [23]

Answer:

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Step-by-step explanation:

The area (A) of the triangle is calculated as

A = $\frac{1}{2}$ absinC

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A = 0.5 × 12 × 7 × sin49° ≈ 31.7 cm² ( to 1 dec. place )

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