Question

The angle of elevation of the top of a mountain at an unknown distance from the base is 30° and at a distance 10 km further off from the mountain along the same line, the angle of elevation is 15°. Determine the height of the Mountain. (use tan 15° =0.27) (pls The answer is supposed to be 5km)

Answer 1

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Answer 2

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✒ ᴀɴsᴡᴇʀ:-

⛄ ʜᴇɪɢʜᴛ ᴏғ ᴛʜᴇ ᴍᴏᴜɴᴛᴀɪɴ :- 5 ᴋᴍ.

✒ sᴛᴇᴘ-ʙʏ-sᴛᴇᴘ ᴇxᴘʟᴀɴᴀᴛɪᴏɴ:-

⛄ ʟᴇᴛ ᴀʙ ʙᴇ ᴛʜᴇ ᴍᴏᴜɴᴛᴀɪɴ ᴏғ ʜᴇɪɢʜᴛ ʜ ᴋɪʟᴏᴍᴇᴛᴇʀs. ʟᴇᴛ ᴄ ʙᴇ ᴀ ᴘᴏɪɴᴛ ᴀᴛ ᴀ ᴅɪsᴛᴀɴᴄᴇ ᴏғ x ᴋᴍ, ғʀᴏᴍ ᴛʜᴇ ʙᴀsᴇ ᴏғ ᴛʜᴇ ᴍᴏᴜɴᴛᴀɪɴ sᴜᴄʜ ᴛʜᴀᴛ ᴛʜᴇ ᴀɴɢʟᴇ ᴏғ ᴇʟᴇᴠᴀᴛɪᴏɴ ᴏғ ᴛʜᴇ ᴛᴏᴘ ᴀᴛ ᴄ ɪs 30°. ʟᴇᴛ ᴅ ʙᴇ ᴀᴛ ᴀ ᴅɪsᴛᴀɴᴄᴇ ᴏғ 10 ᴋᴍ ғʀᴏᴍ ᴄ sᴜᴄʜ ᴛʜᴀᴛ ᴛʜᴇ ᴀɴɢʟᴇ ᴏғ ᴇʟᴇᴠᴀᴛɪᴏɴ ᴀᴛ ᴅ ɪs ᴏғ 15°.

ɪɴ ∆ᴀᴄʙ, ᴡᴇ ʜᴀᴠᴇ

ᴛᴀɴ 30° = ᴀʙ/ᴀᴄ

=> 1/√3 = ʜ/x

=> x = √3ʜ

ɪɴ ∆ᴀᴅʙ, ᴡᴇ ʜᴀᴠᴇ

ᴛᴀɴ 15° = ᴀʙ/ᴀᴅ

=> 0.27 = ʜ/x + 10

=> (0.27)(x + 10) = ʜ ......(ɪ)

sᴜʙsᴛɪᴛᴜᴛɪɴɢ x = √3ʜ ɪɴ ᴇϙᴜᴀᴛɪᴏɴ (ɪ), ᴡᴇ ɢᴇᴛ

0.27 (√3ʜ + 10) = ʜ

=> 0.27 × √3ʜ + 0.27 × 10 = ʜ

=> 2.7 = ʜ - 0.27 × √3ʜ

=> 2.7 = ʜ (1 - 0.27 × √3)

=> 2.7 = ʜ (1 - 0.46)

=> ʜ = 2.7/0.54

=> ʜ = 5

ʜᴇɴᴄᴇ, ᴛʜᴇ ʜᴇɪɢʜᴛ ᴏғ ᴛʜᴇ ᴍᴏᴜɴᴛᴀɪɴ ɪs 5 ᴋᴍ.

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