Question

From a point p on the ground the angle of elevation of the top of a tall building is 30 degree a flag is hosted on the top of the building an angle of elevation of the top of the flagstaff rupees 45 degree find the length of the flagstaff and distance of the building from point p

Answer 1

Answer:

h(√3-1) and h√3

Step-by-step explanation:

hope it helps!!!

pls follow ask if u don't understand this!!

Answer 2

Let AB be the building of height of 10m and BC be the flagstaff of height h metres. P is the point of observation. Then,

$\sf{\angle{APB}=30°\:and\:\angle{APC}=45°}$

From right ∆PAB,we have

$\longrightarrow$$\sf\red{ \tan30° = \frac{AB}{AP}}$

$\longrightarrow$$\sf\red{ \frac{1}{ \sqrt{3} } = \frac{10}{AP}}$

$\longrightarrow$$\sf\red{AP = 10 \sqrt{3}}$

$\longrightarrow$$\sf\red{10 \times 1.732}$

$\longrightarrow$$\sf\red{17.32m}$

Hence, the distance of the building from the point P is 17.32m.

From right ∆PAC, we have

$\longrightarrow$$\sf\green{tan45°=\frac{AC}{AP}}$

$\longrightarrow$$\sf\green{1=\frac{h+10}{10√3}}$

$\therefore$ $\sf\green{h+10=10√3}$

$\longrightarrow$$\sf\green{h = 10( \sqrt{3} - 1)}$

$\longrightarrow$$\sf\green{10(1.732-1}$

$\longrightarrow$$\sf\green{7.32m}$

Hence, the length of the flagstaff is 7.32m.