(B) In $\Delta ABC$,we are given $m \angle A = 90^{\circ}$ and $m \angle B = 30^{\circ}$.Since the sum of angles in a triangle is $180^{\circ}$,$m \an

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(B) In $\Delta ABC$,we are given $m \angle A = 90^{\circ}$ and $m \angle B = 30^{\circ}$.Since the sum of angles in a triangle is $180^{\circ}$,$m \angle C = 180^{\circ} - (90^{\circ} + 30^{\circ}) = 60^{\circ}$.In a right-angled triangle,the side opposite to the $30^{\circ}$ angle is half the length of the hypotenuse.The side opposite to $\angle B$ $(30^{\circ})$ is $AC$,and the hypotenuse is $BC$.Therefore,$AC = \frac{1}{2} BC$.

Class 10 Mathematics Triangles Mix Examples - Triangles

Easy

In $\Delta ABC$,$m \angle A = 90^{\circ}$ and $m \angle B = 30^{\circ}$. Then,which of the following holds true?

A
$AC = \frac{1}{2} AB$
B
$AC = \frac{1}{2} BC$
C
$AB = \frac{1}{2} BC$
D
$AB = \frac{1}{2} AC$

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Mix Examples - Triangles

If $\Delta PQR \sim \Delta XYZ$ under the correspondence $PQR \leftrightarrow YZX$,and $m \angle P = 80^{\circ}$ and $m \angle Q = 40^{\circ}$,find $m \angle Z$. (in $^{\circ}$)

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Prove that if in a triangle the square of one side is equal to the sum of the squares of the other two sides,then the angle opposite the first side is a right angle.

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In $\Delta ABC$,the bisector of $\angle A$ intersects $\overline{BC}$ at $D$. If $AB : AC = 3 : 4$ and $BC = 14$,find $BD$.

Medium

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If $\Delta XYZ \sim \Delta DEF$ for the correspondence $XYZ \leftrightarrow EFD$.
If $m \angle X : m \angle Y : m \angle Z = 2 : 3 : 5$,then in $\Delta DEF$,$\ldots \ldots$ is a right angle.

Medium

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$\Delta PQR \sim \Delta XYZ$ for the correspondence $PQR \leftrightarrow XYZ$. The perimeter of $\Delta PQR$ is $24$ and the perimeter of $\Delta XYZ$ is $60$. If $PR = 10$,find $XZ$.

Medium

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In $\Delta ABC$,$m \angle A = 90^{\circ}$ and $m \angle B = 30^{\circ}$. Then,which of the following holds true?

Similar Questions

If $\Delta PQR \sim \Delta XYZ$ under the correspondence $PQR \leftrightarrow YZX$,and $m \angle P = 80^{\circ}$ and $m \angle Q = 40^{\circ}$,find $m \angle Z$. (in $^{\circ}$)

Prove that if in a triangle the square of one side is equal to the sum of the squares of the other two sides,then the angle opposite the first side is a right angle.

In $\Delta ABC$,the bisector of $\angle A$ intersects $\overline{BC}$ at $D$. If $AB : AC = 3 : 4$ and $BC = 14$,find $BD$.

If $\Delta XYZ \sim \Delta DEF$ for the correspondence $XYZ \leftrightarrow EFD$.If $m \angle X : m \angle Y : m \angle Z = 2 : 3 : 5$,then in $\Delta DEF$,$\ldots \ldots$ is a right angle.

$\Delta PQR \sim \Delta XYZ$ for the correspondence $PQR \leftrightarrow XYZ$. The perimeter of $\Delta PQR$ is $24$ and the perimeter of $\Delta XYZ$ is $60$. If $PR = 10$,find $XZ$.

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If $\Delta XYZ \sim \Delta DEF$ for the correspondence $XYZ \leftrightarrow EFD$.
If $m \angle X : m \angle Y : m \angle Z = 2 : 3 : 5$,then in $\Delta DEF$,$\ldots \ldots$ is a right angle.