AM Indices Surds and Logarithm Practice Q1

Timothy Gan

AM Indices Surds and Logarithm Practice Question 1

The triangle $ABC$ is such that its area is $\frac{1}{4}\left( 12+9\sqrt{3} \right)$ cm$^{2}$, the length of $AB$ is $\left( \sqrt{3}+2 \right)$cm and angle $BAC$ is ${{60}^{\circ }}$. Without using a calculator, find

(i)

the length, in cm, of $AC$ in the form $a+b\sqrt{3}$, where $a$ and $b$ are integers,

(ii)

an expression, in cm$^{2}$, for $B{{C}^{2}}$ in the form $c+d\sqrt{3}$, where $c$ and $d$ are integers.

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AM Indices Surds and Logarithm Practice Q1 AM Indices Surds and Logarithm Practice Q1
AM Indices Surds and Logarithm Practice Q1
AM Indices Surds and Logarithm Practice Q1 AM Indices Surds and Logarithm Practice Q1
AM Indices Surds and Logarithm Practice Q1

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Published: 28th January 2023

Written by

Timothy Gan

This is Tim. Tim loves to teach math. Tim seeks to improve his teaching incessantly! Help Tim by telling him how he can do better.

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