smc-6834-50-Rounding to the Minute

Measurement, STD1 M3 2022 HSC 32

The diagram shows two right-angled triangles, `A B C` and `A B D`,

where `A C=35 \ text{cm}`, `B D=93 \ text{cm}`, `/_ A C B=41^@` and ` /_ A D B=\theta`.

Calculate the size of angle `\theta`, to the nearest minute. (4 marks)

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`19^@6^{′}`

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`text{In}\ Delta ABC:`

`text{In}\ Delta ABD:`

♦♦♦ Mean mark 17%.

Two right-angled triangles, `ABC` and `ADC`, are shown.

Calculate the size of angle `theta`, correct to the nearest minute. (3 marks)

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`41^@5^{′}\ text{(nearest minute)}`

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`text(Using Pythagoras in)\ DeltaACD:`

♦♦♦ Mean mark 15%.

`text(In)\ DeltaABC:`

The diagram shows a right-angled triangle.

What is the value of `theta`, to the nearest minute?

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`B`

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`tan theta`	`= text(opp)/text(adj)`
	`= 5.3/1.9= 2.789\ …`

COMMENT: An angle that has over 30″ (seconds) is rounded up to the next minute (i.e. rounded up to 70°17′).

`:. theta`	`= 70.277\ …^@`
	`=70°16^{′}39.8^{″}~~ 70^@17^{′}`

`=>B`

Use Pythagoras’ theorem to show that `ΔABC` is a right-angled triangle. (1 mark)

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Calculate the size of `∠ABC` to the nearest minute. (2 marks)

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a. `text(Proof)`

b. `67°23^{′}`

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a. `ΔABC\ text(is right-angled if)\ \ a^2 + b^2 = c^2`

MARKER’S COMMENT: Know your calculator process for producing an angle in minutes/seconds. Note >30 “seconds” rounds up to the higher “minute”.

b. `sin ∠ABC = 12/13`