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Triangles — Maths STD 9 — Question

Gujarat BoardEnglish MediumSTD 9MathsTriangles4 Marks
Question
Read the Source/ Text given below and answer any four questions: In a forest, a big tree got broken due to heavy rain and wind. Due to this rain the big branches $AB$ and $AC$ with lengths $5\ m$ fell down on the ground. Branch $AC$ makes an angle of $30^\circ $ with the main tree $AP.$ The distance of Point $B$ from $P$ is $4\ m.$ You can observe that $\triangle\text{ABP}$ is congruent to $\triangle\text{ACP}.$

Now answer the following questions:
$i. \triangle\text{ACP}$ and $\triangle\text{ABP}$ are congruent by which criteria?
$a. \text{SSS}$
$b. \text{SAS}$
$c.\text{ASA}$
$d. \text{RHS}$
$ii.$ What is the length of $CP?$
$a.4\ m$
$b.5\ m$
$c.3\ m$
$d.10\ m$
$iii.$ What is the value of $\angle\text{BAP}?$
$a.40^\circ $
$b.50^\circ $
$c.30^\circ $
$d.60^\circ $
$iv.$ What is the value of $\angle\text{APB}?$
$a.40^\circ $
$b.50^\circ $
$c.60^\circ $
$d.90^\circ $
$v.$ What is the height of the remaining tree$?$
$a.4\ m$
$5\ m$
$c.3\ m$
$d.10\ m$
✓

Answer

$i$ $d$ $RHS$
$ii$ $a$ $4m$
$iii$ $c$ $30^\circ $
$iv$ $d$ $90^\circ $
$v$ $c$ $3m$

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