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Important three-dimensional problems based on triangular prism IGCSE/GCSE Trigonometry 0580 Extended
Sat Mar 2, 2024
Important three-dimensional problem based on triangular prism IGCSE/GCSE Trigonometry 0580 Extended
Question: The diagram shows a triangular prism. The base, ABCD, of the prism is a square of side length 15 cm. ∟ABE and ∟CBE are right angles. ∟EAB=35°. M is the point on DA such that DM: MA=2:3. Calculate the size of the angle between
EM and the base of the prism.
Solution: After working on given figure
Now M is a point on DA such that DM: MA=2:3
So, MD=(2/5 )×15= 6 cm and MA=(3/5 )×15= 9 cm
Since we have to find the size of the angle between EM and the base of the prism, so question is to find the size of ∟θ.
To find ∟θ from ∆EMB, we require sides EM and BM.
For finding EM, consider the right ∆EBA,
Tan 35°=EB/15 EB= 15× Tan 35°=10.5 cm
For finding MB, consider the right ∆AMB, applying Pythagoras theorem,
MB²=15²+9²=306
MB=√306=17.5 cm
Now for finding ∟θ from ∆EMB,
Tan θ =10.5/17.5 =0.6
θ=Tan⁻¹ 0.6 =31°
∟EMB=31°
So, the size of the angle between EM and the base of the prism=31°
Ruchi Chhabra
Hi! I’m Ruchi. Graduate in Maths major from Lady Shri Ram College, Postgraduate in O.R. from Hansraj College DU. Teaching Math to high school students of IB, ICSE & CBSE boards and expert in teaching Vedic Math & Quant’s section of different competitive exams like CAT, SAT, GMAT, GRE, CLAT, NTSE and Math Olympiads, etc. Instructor of many Bestselling Courses in Math on Udemy.
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