angle $z$ is the perpendicular height: $\\text{Opposite} = 17.5 \\text{ m}$\n* **Hypotenuse** is the side: $\\text{Hypotenuse} = 25 \\text{ m}$","highlights":[{"text":"25 m","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$\\sin(z) = \\frac{\\text{Opposite}}{\\text{Hypotenuse}}$"},{"latex":"$$\\sin(z) = \\frac{\\htmlData{anchor=opp-val}{\\color{@sky}{17.5}}}{\\htmlData{anchor=hyp-val}{\\color{@amber}{25}}}$"},{"latex":"$$\\sin(z) = \\htmlData{anchor=sin-val}{\\color{@purple}{0.7}}$"}],"highlights":[{"color":"sky","style":"text-color","anchor":"opp-val"},{"color":"amber","style":"text-color","anchor":"hyp-val"},{"color":"purple","style":"text-color","anchor":"sin-val"}],"connections":[{"to":"sin-val","from":"opp-val","color":"sky","label":null,"style":"solid"},{"to":"sin-val","from":"hyp-val","color":"amber","label":null,"style":"solid"}]},"order":3,"title":"Set up trigonometric ratio","description":"We use the sine ratio ($\\text{SOH}$) from trigonometry since we know the opposite side and the hypotenuse."},{"type":"text","order":4,"title":"Solve for angle z","content":"To find $z$, we take the inverse sine of both sides:\n\n$$z = \\sin^{-1}(0.7)$$\n\nUsing a calculator:\n\n$$z \\approx 44.427...^\\circ$$\n\nRounding to **1 decimal place** as requested:\n\n$$z = 44.4^\\circ$$","calculator":[{"gdc":{"expression":"\\sin^{-1}(0.7)","instructions":"1. Set the angle mode to Degrees in settings.\n2. In the run-matrix menu, type asin(0.7) or sin⁻¹(0.7) and press [EXE]."},"ti84":{"expression":"\\sin^{-1}(0.7)","instructions":"1. Ensure your calculator is in DEGREE mode by pressing [MODE], selecting 'DEGREE', and pressing [ENTER].\n2. Press [2nd] [SIN] to select sin⁻¹.\n3. Type 0.7 and press [ENTER]."},"desmos":{"expression":"\\arcsin(0.7)","instructions":"1. Click the wrench icon in the top-right corner and ensure 'Degrees' is selected.\n2. Type arcsin(0.7) or sin^(-1)(0.7) into the input line."},"description":"Calculate the inverse sine to find the angle in degrees."}],"highlights":[{"text":"Give your answer to 1 decimal place","location":"specification"}]}]}],"generatedAt":"2026-06-12T18:31:46.069Z","modelVersion":"gemini-3.5-flash","explanationVersion":"v2"},"firstAttemptFullMarks":null,"walkthroughVideo":null},{"id":"77986c94-4d61-422d-8d38-68b81c779807","revisionId":"55f7edc6-23ef-43c2-be3a-fb53140e1952","questionNumber":null,"questionType":"LA","specification":"![A triangular banner has two sides of length (x + 4) cm and (x + 6) cm, with an included angle of 60 degrees.](https://assets.mathsgenie.co.uk/question-image-redraws/sol-max-v1/77986c94-4d61-422d-8d38-68b81c779807/image-1-1eea0b65aa13563fd919dbc3.svg)","difficulty":4,"difficultyBand":"medium","totalMarks":5,"sourceTitle":null,"calculatorUse":"calc","isCalculation":true,"parts":[{"id":"caf8a4f3-b029-4a64-bc2d-09eed73893fa","label":"a","content":"The area of the banner is $40 \\text{ cm}^2$. \nWork out the value of $x$. \nGive your answer to 3 significant figures.","markscheme":"- Sets up equation: $\\frac{1}{2}(x+4)(x+6)\\sin(60) = 40$ M1\n- Simplifies to $x^2 + 10x + 24 = \\frac{80}{\\sin(60)}$ or $x^2 + 10x + 24 \\approx 92.376$ M1\n- Forms quadratic $x^2 + 10x - 68.376... = 0$ M1\n- Applies quadratic formula $x = \\frac{-10 \\pm \\sqrt{10^2 - 4(1)(-68.376)}}{2}$ M1\n- Calculates $x = 4.66$ A1","marks":5,"order":0,"markingRubric":{"totalMarks":5,"points":[{"id":"p1","marks":1,"description":"Initial setup of area formula with substituted side and angle values.","code":"M"},{"id":"p2","marks":1,"description":"Algebraic expansion of (x+4)(x+6).","code":"M"},{"id":"p3","marks":1,"description":"Consolidation into a quadratic equation equal to zero.","code":"M"},{"id":"p4","marks":1,"description":"Correct application of a solving method for the quadratic.","code":"M"},{"id":"p5","marks":1,"description":"Final answer for x to 3 significant figures.","code":"A"}],"finalAnswers":["4.66"],"generatedAt":"2026-05-06T14:01:37.114Z","modelVersion":"gemini-3-flash

Finding the Area of Any Triangle

Question 16

Finding the Area of Any Triangle Questions

Finding the Area of Any Triangle

Question 16

Finding the Area of Any Triangle Questions