Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
0 votes
13.5k views
in Mathematics by (58.2k points)

A monument ABCD stands on a level ground. At a point P on the ground, the portion AB, AC and AD subtends angles αβ and γ respectively. If AB = a, AC = b, AD = c, AP = x and α+β+γ = 180°, show that (a + b + c)x2 = abc. A being on the ground.

1 Answer

+1 vote
by (54.5k points)
selected by
 
Best answer

Let AD = monument, with foot at A 

P = point of observation 

Given AB = a, AC = b, AD = c, AP = x 

and α+β+γ = 180°

From ΔAPB, tanα = a/x 

From ΔAPC, tanβ = b/x 

From ΔAPD, tanγ = c/x 

Since α+β+γ = 180° => S1 = S3 

=> tanα + tanβ + tanγ = tanα . tanβ . tanγ

=> x2 (a + b + c) = abc.

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

Categories

...