Question

A triangle has sides 8cm and 5cm and an angle of 90 between them Calculate
the smallest angle of the triangle​

Answer 1

Answer:

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Answer 2

Answer:

The smallest angle of the triangle is $32$°.

Step-by-step explanation:

Step 1 of 3

Constructing the triangle using given measurements.

Given: one side of the triangle (say) $AB$ = 8 cm

The other side of the triangle (say) $BC$ = 5 cm

Angle between $AB$ and $BC$ = 90°

⇒ ∠$ABC =90$°

This means sides $AB$ and $BC$ are perpendicular to each other.

Hence Δ$ABC$ is a right angled triangle.

Let $x$ and $y$ are the other $2$ angles of the triangle.

Step 2 of 3

Compute the angle $x$ as follows:

Using trigonometric function,

$tanx=\frac{AB}{BC}$

$tanx=\frac{8}{5}$

$x=tan_{-1}(\frac{8}{5})$

$x=58$° (approx.)

Step 3 of 3

Compute the angle $y$ as follows:

Using trigonometric function,

$tany=\frac{BC}{AB}$

$tany=\frac{5}{8}$

$y=tan_{-1}(\frac{5}{8})$

$y=32$°

Final answer: The smallest angle of the triangle is $32$°.

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