In a right-angled triangle the hypotenuse is 15 cm and one acute angle θ satisfies θ = 0.6. What is the length of the side opposite θ?

Worked solution for TMUA-P1-MGEO-005 is revealed on this page behind the solution details.

Why isn't the answer to TMUA-P1-MGEO-005 shown upfront?

The options are lettered without marking the correct one so you attempt TMUA-P1-MGEO-005 first — TMUA questions reward spotting the trap before you check the worked solution below.

Do I need a calculator for TMUA-P1-MGEO-005?

No — calculators are banned in the TMUA. TMUA-P1-MGEO-005 is set for a no-calculator target of about 180 seconds; the worked solution shows the fastest by-hand route.

Which TMUA specification point is TMUA-P1-MGEO-005?

TMUA-P1-MGEO-005 is Paper P1 · Geometry (specification code M-Geo), level 2. Drill more of the same topic from this page.

TMUA-P1-MGEO-005 — Paper P1 · Geometry · Level 2

P1M-GeoLevel 2~180s target

Spec: M-Geo · No calculator · ~180s

In a right-angled triangle the hypotenuse is

15

cm and one acute angle

\theta

satisfies

\sin\theta = 0.6

. What is the length of the side opposite

\theta

Options

$25$
$12$
$9$
$7.5$
$0.6$

Letters only — the answer key is hidden. Work it out, then check the solution below.

Hint (check trope)

No written hint yet — check the trope: trig-ratios, rearrangement-trap. Name the trap first, work the stem by hand, then open the solution below.

Show solution

Opposite

= \text{hypotenuse} \times \sin\theta = 15 \times 0.6 = 9

. Trap:

25

divides (

15 / 0.6

) instead of multiplying — plausible if you rearrange SOHCAHTOA the wrong way.

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Keep practising

Same topic · same level

P1M-GeoLevel 2

TMUA-P1-MGEO-004

A cuboid measures 3 cm by 4 cm by 12 cm. What is the length of its space diagonal?

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Open TMUA-P1-MGEO-004 →

Same trap: trig-ratios

P1M-GeoLevel 1

TMUA-P1X-MGEO-02

In a right-angled triangle the hypotenuse is 13 cm and the side opposite angle θ is 5 cm. What is θ?

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Open TMUA-P1X-MGEO-02 →

Step up a level

P1M-GeoLevel 3

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A right circular cone has base radius 5 cm and slant height 13 cm. What is its volume in cm ^3?

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Open TMUA-P1-MGEO-009 →

TMUA-P1-MGEO-005 — Paper P1 · Geometry · Level 2

Options

Keep practising

Master Geometry

TMUA-P1-MGEO-005 — Paper P1 · Geometry · Level 2

Options

Keep practising

Master Geometry