In triangle ABC, angle A = 30^°, angle B = 90^° and side a = 5. What is the length of side b?

Worked solution for TMUA-P1-MM4-003 is revealed on this page behind the solution details.

Why isn't the answer to TMUA-P1-MM4-003 shown upfront?

The options are lettered without marking the correct one so you attempt TMUA-P1-MM4-003 first — TMUA questions reward spotting the trap before you check the worked solution below.

Do I need a calculator for TMUA-P1-MM4-003?

No — calculators are banned in the TMUA. TMUA-P1-MM4-003 is set for a no-calculator target of about 150 seconds; the worked solution shows the fastest by-hand route.

Which TMUA specification point is TMUA-P1-MM4-003?

TMUA-P1-MM4-003 is Paper P1 · Trigonometry (specification code MM4), level 1. Drill more of the same topic from this page.

TMUA-P1-MM4-003 — Paper P1 · Trigonometry · Level 1

P1MM4Level 1~150s target

Spec: MM4 · No calculator · ~150s

In triangle

ABC

, angle

A = 30^\circ

, angle

B = 90^\circ

and side

a = 5

. What is the length of side

b

Options

$2.5$
$5$
$5\sqrt{3}$
$10$
$20$

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: sine-rule. Name the trap first, work the stem by hand, then open the solution below.

Show solution

By the sine rule

\frac{b}{\sin 90^\circ} = \frac{5}{\sin 30^\circ}

, so

b = 5 / \frac{1}{2} = 10

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Keep practising

Same topic · same level

P1MM4Level 1

TMUA-P1-MM4-001

What is the exact value of 60^°?

Trigonometry

Open TMUA-P1-MM4-001 →

Step up a level

P1MM4Level 2

TMUA-P1-MM4-005

A triangle has sides of length 5 and 7 with included angle 60^°. What is the length of the third side?

Trigonometry

Open TMUA-P1-MM4-005 →

TMUA-P1-MM4-003 — Paper P1 · Trigonometry · Level 1

Options

Keep practising

Master Trigonometry

TMUA-P1-MM4-003 — Paper P1 · Trigonometry · Level 1

Options

Keep practising

Master Trigonometry