Question

a carefully andanswer thequestions: 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 5m fell down on the ground. Branch AC makes an angle of 30° with the main tree AP. The distance of point B from P is 4 m. you can observe that AABP is congruent to ACP.
1...ACP and ABP are congruent by which criteria?
2... what is the length of CP?
a3m b4m c10m d5m
3...what is the value of angle bap
A 40 degree b 50 degree c 60 degree d 90 degree
what is the height of the remaining tree
a 3m b 4m c 5m d 10m.​

Answer 1

Step-by-step explanation:

• Given: $AB=5m$

                   $\\AC= 5m$

                   $\angle CAP = 30^\circ$

                   $BP=4m$

                   $\triangle ABP \cong \triangle ACP$

• To Find: The criterion for Congruency

                       Length of CP

                       Value of $\angle BAP$

                       Height of the remaining tree

• We know, In geometry, two figures or objects are said to be congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other. They will be perfectly aligned.
• Since it is given that $\triangle ABP \cong \triangle ACP$,  Also,

         ⇒ $AB=5m=AC$            [Given - Hypotenuse]

         ⇒ $AP=AP$                       [Common - Side]

         ⇒ $\angle BPA = 90^\circ=\angle CPA$  [Tree makes an angle of 90° with ground -   Right Angle]

Therefore, The criterion for congruency here is RHS - Two right triangles are congruent if the hypotenuse and one side of one triangle are equal to the corresponding hypotenuse and one side of the other triangle.

• Since it is given that $\triangle ABP \cong \triangle ACP$, then CP corresponds to BP, i.e., $BP=CP=4m$

Hence, the length of CP is (b) $4m.$

• Since it is given that $\triangle ABP \cong \triangle ACP$, then $\angle CAP$ corresponds to $\angle BAP$, i.e., $\angle CAP = 30^\circ=\angle BAP$

Hence, The value of $\angle BAP$ is also $30^\circ$.

• By Pythagoras theorem of Right Angles,

        ⇒ $Hypotenuse^2=Perpendicular^2+Base^2$

• In $\triangle ACP, H=5, B=4\ and\ P=?$

• By Putting the values in the formula, we get,

        ⇒ $5^2=4^2+P^2$

        ⇒ $25-16=P^2$

        ⇒ $9=P^2$

        ⇒ $\sqrt{9}=3=P$

Hence, the height of the remaining tree is (a) 3m

Answer 2

Answer:

Step-by-step explanation:

1.RHS

2.3m

3.40°

4.4m